Functions & Relations - Algebra

Card 0 of 36

Find the composition, $f\circ g$ given

Tap to see back →

To find the composition, $f\circ g$ given

recall what a composition of two functions represents.

$f \circ g=f(g(x))$

This means that the function will replace each in the function .

Therefore, in this particular problem the composition becomes

$\f\circ g=f(g(x)) $\f(g(x))=(3x)^2$+2(3x) $\f(g(x))=9x^2$+6x$

Find the inverse of .

$f(x)=\frac{3}{2+5x}$$

Tap to see back →

To find the inverse of a function swap the variables and solve for . The function and its inverse when multiplied together, equals one. This means that the inverse undoes the function.

For this particular function the inverse is found as follows.

$f(x)=\frac{3}{2+5x}$$

$y=\frac{3}{2+5x}$$

First, switch the variables.

$x=\frac{3}{2+5y}$$

Now, perform algebraic operations to solve for .

$x\cdot (2+5y)={3}$

$\frac{x\cdot(2+5y)}{x}$=\frac{3}{x}$

$\2+5y=\frac{3}{x}$ \5y=\frac{3}{x}$-2 \y=\frac{3}{5x}$-$\frac{2}{5}$$

Therefore, the inverse is

Find the composition, $f\circ g$ given

Tap to see back →

To find the composition, $f\circ g$ given

recall what a composition of two functions represents.

$f \circ g=f(g(x))$

This means that the function will replace each in the function .

Therefore, in this particular problem the composition becomes

$\f\circ g=f(g(x)) $\f(g(x))=2(7x)^2$+3 $\f(g(x))=2(49x^2$$)+3\f(g(x))=98x^2$+3$

Find the inverse of the function .

Tap to see back →

To find the inverse of a function swap the variables and solve for . The function and its inverse when multiplied together, equals one. This means that the inverse undoes the function.

For this particular function the inverse is found as follows.

First, switch the variables.

Now, perform algebraic operations to solve for .

Therefore, the inverse is

Find the composition, $f\circ g$ given

Tap to see back →

To find the composition, $f\circ g$ given

recall what a composition of two functions represents.

$f \circ g=f(g(x))$

This means that the function will replace each in the function .

Therefore, in this particular problem the composition becomes

$\f\circ g=f(g(x)) \f(g(x))=\left($\frac{1}{2}$x \right $)^2$$\f(g(x))=\frac{1}{4}$x^2$$

Find the composition, $f\circ g$ given

Tap to see back →

To find the composition, $f\circ g$ given

recall what a composition of two functions represents.

$f \circ g=f(g(x))$

This means that the function will replace each in the function .

Therefore, in this particular problem the composition becomes

$\f\circ g=f(g(x)) $\f(g(x))=(3x)^2$+2(3x) $\f(g(x))=9x^2$+6x$

Find the inverse of .

$f(x)=\frac{3}{2+5x}$$

Tap to see back →

To find the inverse of a function swap the variables and solve for . The function and its inverse when multiplied together, equals one. This means that the inverse undoes the function.

For this particular function the inverse is found as follows.

$f(x)=\frac{3}{2+5x}$$

$y=\frac{3}{2+5x}$$

First, switch the variables.

$x=\frac{3}{2+5y}$$

Now, perform algebraic operations to solve for .

$x\cdot (2+5y)={3}$

$\frac{x\cdot(2+5y)}{x}$=\frac{3}{x}$

$\2+5y=\frac{3}{x}$ \5y=\frac{3}{x}$-2 \y=\frac{3}{5x}$-$\frac{2}{5}$$

Therefore, the inverse is

Find the composition, $f\circ g$ given

Tap to see back →

To find the composition, $f\circ g$ given

recall what a composition of two functions represents.

$f \circ g=f(g(x))$

This means that the function will replace each in the function .

Therefore, in this particular problem the composition becomes

$\f\circ g=f(g(x)) $\f(g(x))=2(7x)^2$+3 $\f(g(x))=2(49x^2$$)+3\f(g(x))=98x^2$+3$

Find the inverse of the function .

Tap to see back →

To find the inverse of a function swap the variables and solve for . The function and its inverse when multiplied together, equals one. This means that the inverse undoes the function.

For this particular function the inverse is found as follows.

First, switch the variables.

Now, perform algebraic operations to solve for .

Therefore, the inverse is

Find the composition, $f\circ g$ given

Tap to see back →

To find the composition, $f\circ g$ given

recall what a composition of two functions represents.

$f \circ g=f(g(x))$

This means that the function will replace each in the function .

Therefore, in this particular problem the composition becomes

$\f\circ g=f(g(x)) $\f(g(x))=(3x)^2$+2(3x) $\f(g(x))=9x^2$+6x$

Find the inverse of .

$f(x)=\frac{3}{2+5x}$$

Tap to see back →

To find the inverse of a function swap the variables and solve for . The function and its inverse when multiplied together, equals one. This means that the inverse undoes the function.

For this particular function the inverse is found as follows.

$f(x)=\frac{3}{2+5x}$$

$y=\frac{3}{2+5x}$$

First, switch the variables.

$x=\frac{3}{2+5y}$$

Now, perform algebraic operations to solve for .

$x\cdot (2+5y)={3}$

$\frac{x\cdot(2+5y)}{x}$=\frac{3}{x}$

$\2+5y=\frac{3}{x}$ \5y=\frac{3}{x}$-2 \y=\frac{3}{5x}$-$\frac{2}{5}$$

Therefore, the inverse is

Find the composition, $f\circ g$ given

Tap to see back →

To find the composition, $f\circ g$ given

recall what a composition of two functions represents.

$f \circ g=f(g(x))$

This means that the function will replace each in the function .

Therefore, in this particular problem the composition becomes

$\f\circ g=f(g(x)) $\f(g(x))=2(7x)^2$+3 $\f(g(x))=2(49x^2$$)+3\f(g(x))=98x^2$+3$

Find the inverse of the function .

Tap to see back →

To find the inverse of a function swap the variables and solve for . The function and its inverse when multiplied together, equals one. This means that the inverse undoes the function.

For this particular function the inverse is found as follows.

First, switch the variables.

Now, perform algebraic operations to solve for .

Therefore, the inverse is

Find the composition, $f\circ g$ given

Tap to see back →

To find the composition, $f\circ g$ given

recall what a composition of two functions represents.

$f \circ g=f(g(x))$

This means that the function will replace each in the function .

Therefore, in this particular problem the composition becomes

$\f\circ g=f(g(x)) \f(g(x))=\left($\frac{1}{2}$x \right $)^2$$\f(g(x))=\frac{1}{4}$x^2$$

Find the composition, $f\circ g$ given

Tap to see back →

To find the composition, $f\circ g$ given

recall what a composition of two functions represents.

$f \circ g=f(g(x))$

This means that the function will replace each in the function .

Therefore, in this particular problem the composition becomes

$\f\circ g=f(g(x)) $\f(g(x))=(3x)^2$+2(3x) $\f(g(x))=9x^2$+6x$

Find the inverse of .

$f(x)=\frac{3}{2+5x}$$

Tap to see back →

To find the inverse of a function swap the variables and solve for . The function and its inverse when multiplied together, equals one. This means that the inverse undoes the function.

For this particular function the inverse is found as follows.

$f(x)=\frac{3}{2+5x}$$

$y=\frac{3}{2+5x}$$

First, switch the variables.

$x=\frac{3}{2+5y}$$

Now, perform algebraic operations to solve for .

$x\cdot (2+5y)={3}$

$\frac{x\cdot(2+5y)}{x}$=\frac{3}{x}$

$\2+5y=\frac{3}{x}$ \5y=\frac{3}{x}$-2 \y=\frac{3}{5x}$-$\frac{2}{5}$$

Therefore, the inverse is

Find the composition, $f\circ g$ given

Tap to see back →

To find the composition, $f\circ g$ given

recall what a composition of two functions represents.

$f \circ g=f(g(x))$

This means that the function will replace each in the function .

Therefore, in this particular problem the composition becomes

$\f\circ g=f(g(x)) $\f(g(x))=2(7x)^2$+3 $\f(g(x))=2(49x^2$$)+3\f(g(x))=98x^2$+3$

Find the inverse of the function .

Tap to see back →

To find the inverse of a function swap the variables and solve for . The function and its inverse when multiplied together, equals one. This means that the inverse undoes the function.

For this particular function the inverse is found as follows.

First, switch the variables.

Now, perform algebraic operations to solve for .

Therefore, the inverse is

Find the composition, $f\circ g$ given

Tap to see back →

To find the composition, $f\circ g$ given

recall what a composition of two functions represents.

$f \circ g=f(g(x))$

This means that the function will replace each in the function .

Therefore, in this particular problem the composition becomes

$\f\circ g=f(g(x)) $\f(g(x))=(3x)^2$+2(3x) $\f(g(x))=9x^2$+6x$

Find the inverse of .

$f(x)=\frac{3}{2+5x}$$

Tap to see back →

To find the inverse of a function swap the variables and solve for . The function and its inverse when multiplied together, equals one. This means that the inverse undoes the function.

For this particular function the inverse is found as follows.

$f(x)=\frac{3}{2+5x}$$

$y=\frac{3}{2+5x}$$

First, switch the variables.

$x=\frac{3}{2+5y}$$

Now, perform algebraic operations to solve for .

$x\cdot (2+5y)={3}$

$\frac{x\cdot(2+5y)}{x}$=\frac{3}{x}$

$\2+5y=\frac{3}{x}$ \5y=\frac{3}{x}$-2 \y=\frac{3}{5x}$-$\frac{2}{5}$$

Therefore, the inverse is