Evaluate Functions - Pre-Calculus

Card 0 of 40

Given and , evaluate .

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We are given two functions and asked to find f(h(7)).

I would begin by finding h(7)

Now that we know h(7), we go ahead and plug it into f(x).

$f(0)=5\cdot $0^2$-13\cdot 0+8=8$

So our final answer is simply 8.

Solve the function.

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Determine the domain of .

$x\neq1$

Multiply on both sides of the equation to cancel the denominator and divide the equation by ten.

$x= \pm1$

Since the domain states that $x\neq1$ , the only possible answer is .

Solve for :

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Rewrite so that the exponential variable is isolated.

Reconvert to a similar base. Use exponents to redefine the terms.

Since all terms are of the same base, use the property of log to eliminate the base on both sides of the equation.

Solve for .

$x=\frac{1}{2}$$

Determine the value of of the function

$f(x)=$\sqrt{71-x}$$

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In order to determine the value of of the function we set The value becomes

$f(7)=$\sqrt{71-7}$=$\sqrt{64}$=8$

As such

Evaluate the following function when

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Evaluate the following function when

To evaluate this function, simply plug-in 6 for t and simplify:

So our answer is:

Evaluate for $x=\frac{3\pi}{4}$$ .

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We evaluate the function when $x=\frac{3\pi}{4}$$ .

Find the value of the following function when

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Find the value of the following function when

To evaluate this function, plug in 2 for x everywhere it arises and simplify:

So our answer must be undefined, because we cannot divide by

Find the value of when $t=\frac{3\pi}{4}$$

$g(t)=5\cos(t)-5\sin(t)$

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Find the value of when $t=\frac{3\pi}{4}$$

$g(t)=5\cos(t)-5\sin(t)$

To evaluate this expression, plug in the given value of everywhere you see a and simplify:

$g($\frac{3\pi}{4}$)=5\cos($\frac{3\pi}{4}$)-5\sin($\frac{3\pi}{4}$)=5($\frac{-\sqrt{2}$}{2}-$\frac{\sqrt{2}$}{2})=5($\frac{-2\sqrt{2}$}{2})=-5$\sqrt{2}$$

$5($\frac{-2\sqrt{2}$}{2})=-5$\sqrt{2}$$

So our answer is:

$-5$\sqrt{2}$$

Find the difference quotient of the function .

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Difference quotient equation is

$\frac{f(x+h)-f(x)}{h}$ and

.

Now plug in the appropriate terms into the equation and simplify:

$\ $\frac{f(x+h)-f(x)}{h}$\ $\=\frac{3(x+h)^2$$-2(x+h)-5-(3x^2$-2x-5)}{h}$\ $\=\frac{3(x^2$$+2xh+h^2$$)-2x-2h-5-3x^2$+2x+5}{h}$\ $\=\frac{3x^2$$+6xh+3h^2$$-2x-2h-5-3x^2$+2x+5}{h}$\ $\=\frac{6xh+3h^2$-2h}{h}$\ \=\frac{h(3h+6x-2)}{h}$\ \=3h+6x-2$

If , what is ?

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In order to evaluate this function, simply substitute the value of as a replacement of .

Simplify using the order of operations.

The answer is:

Given and , evaluate .

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We are given two functions and asked to find f(h(7)).

I would begin by finding h(7)

Now that we know h(7), we go ahead and plug it into f(x).

$f(0)=5\cdot $0^2$-13\cdot 0+8=8$

So our final answer is simply 8.

Solve the function.

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Determine the domain of .

$x\neq1$

Multiply on both sides of the equation to cancel the denominator and divide the equation by ten.

$x= \pm1$

Since the domain states that $x\neq1$ , the only possible answer is .

Solve for :

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Rewrite so that the exponential variable is isolated.

Reconvert to a similar base. Use exponents to redefine the terms.

Since all terms are of the same base, use the property of log to eliminate the base on both sides of the equation.

Solve for .

$x=\frac{1}{2}$$

Determine the value of of the function

$f(x)=$\sqrt{71-x}$$

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In order to determine the value of of the function we set The value becomes

$f(7)=$\sqrt{71-7}$=$\sqrt{64}$=8$

As such

Evaluate the following function when

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Evaluate the following function when

To evaluate this function, simply plug-in 6 for t and simplify:

So our answer is:

Evaluate for $x=\frac{3\pi}{4}$$ .

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We evaluate the function when $x=\frac{3\pi}{4}$$ .

Find the value of the following function when

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Find the value of the following function when

To evaluate this function, plug in 2 for x everywhere it arises and simplify:

So our answer must be undefined, because we cannot divide by

Find the value of when $t=\frac{3\pi}{4}$$

$g(t)=5\cos(t)-5\sin(t)$

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Find the value of when $t=\frac{3\pi}{4}$$

$g(t)=5\cos(t)-5\sin(t)$

To evaluate this expression, plug in the given value of everywhere you see a and simplify:

$g($\frac{3\pi}{4}$)=5\cos($\frac{3\pi}{4}$)-5\sin($\frac{3\pi}{4}$)=5($\frac{-\sqrt{2}$}{2}-$\frac{\sqrt{2}$}{2})=5($\frac{-2\sqrt{2}$}{2})=-5$\sqrt{2}$$

$5($\frac{-2\sqrt{2}$}{2})=-5$\sqrt{2}$$

So our answer is:

$-5$\sqrt{2}$$

Find the difference quotient of the function .

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Difference quotient equation is

$\frac{f(x+h)-f(x)}{h}$ and

.

Now plug in the appropriate terms into the equation and simplify:

$\ $\frac{f(x+h)-f(x)}{h}$\ $\=\frac{3(x+h)^2$$-2(x+h)-5-(3x^2$-2x-5)}{h}$\ $\=\frac{3(x^2$$+2xh+h^2$$)-2x-2h-5-3x^2$+2x+5}{h}$\ $\=\frac{3x^2$$+6xh+3h^2$$-2x-2h-5-3x^2$+2x+5}{h}$\ $\=\frac{6xh+3h^2$-2h}{h}$\ \=\frac{h(3h+6x-2)}{h}$\ \=3h+6x-2$

If , what is ?

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In order to evaluate this function, simply substitute the value of as a replacement of .

Simplify using the order of operations.

The answer is: