GRE Math : How to find f(x)

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Example Questions

Example Question #1 : Algebraic Functions

If f(x)=3x and g(x)=2x+2, what is the value of f(g(x)) when x=3?

Possible Answers:

Correct answer:

Explanation:

With composition of functions (as with the order of operations) we perform what is inside of the parentheses first. So, g(3)=2(3)+2=8 and then f(8)=24.

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Example Question #1 : Algebraic Functions

g(x) = 4x – 3

h(x) = .25πx + 5

If f(x)=g(h(x)). What is f(1)?

Possible Answers:

19π – 3

13π + 3

π + 17

Correct answer:

π + 17

Explanation:

First, input the function of h into g. So f(x) = 4(.25πx + 5) – 3, then simplify this expression f(x) = πx + 20 – 3 (leave in terms of π since our answers are in terms of π). Then plug in 1 for x to get π + 17.

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Example Question #2 : Algebraic Functions

If 7y = 4x - 12, then x =

Possible Answers:

(7y+3)/12

(7y+12)/4

(7y+12)/3

(7y-12)/4

Correct answer: (7y+12)/4

Explanation:

Adding 12 to both sides and dividing by 4 yields (7y+12)/4.

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Example Question #1 : How To Find F(X)

f(x) = x^2 + 32x -12

What is f(4) ?

Possible Answers:

156

128

130

132

144

Correct answer:

132

Explanation:

f(x) = x^2 + 32x -12

f(4) = 4^2 + 32(4) -12

= 16 + 128 -12

= 132

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Example Question #4 : How To Find F(X)

If F(x) = 2x² + 3 and G(x) = x – 3, what is F(G(x))?

Possible Answers:

2x² + 12x +18

6x² + 5x

2x² – 12x +21

2x²

6x² – 12x

Correct answer:

2x² – 12x +21

Explanation:

A composite function substitutes one function into another function and then simplifies the resulting expression. F(G(x)) means the G(x) gets put into F(x).

F(G(x)) = 2(x – 3)² + 3 = 2(x² – 6x +9) + 3 = 2x² – 12x + 18 + 3 = 2x² – 12x + 21

G(F(x)) = (2x² +3) – 3 = 2x²

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Example Question #3 : Algebraic Functions

If a(x) = 2x³+ x, and b(x) = –2x, what is a(b(2))?

Possible Answers:

128

132

503

–132

–503

Correct answer:

–132

Explanation:

When functions are set up within other functions like in this problem, the function closest to the given variable is performed first. The value obtained from this function is then plugged in as the variable in the outside function. Since b(x) = –2x, and x = 2, the value we obtain from b(x) is –4. We then plug this value in for x in the a(x) function. So a(x) then becomes 2(–4³) + (–4), which equals –132.

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Example Question #2 : Algebraic Functions

Let F(x) = x³ + 2x² – 3 and G(x) = x + 5. Find F(G(x))

Possible Answers:

x³ + x² + 2

x³ + 2x² – x – 8

x³ + 2x² + x + 2

x³ + x² + x + 8

x³ + 17x² + 95x + 172

Correct answer:

x³ + 17x² + 95x + 172

Explanation:

F(G(x)) is a composite function where the expression G(x) is substituted in for x in F(x)

F(G(x)) = (x + 5)³ + 2(x + 5)² – 3 = x³ + 17x² + 95x + 172

G(F(x)) = x³ + x² + 2

F(x) – G(x) = x³ + 2x² – x – 8

F(x) + G(x) = x³ + 2x² + x + 2

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Example Question #3 : Algebraic Functions

What is the value of xy²(xy – 3xy) given that x = –3 and y = 7?

Possible Answers:

2881

3565

–2881

–6174

Correct answer:

–6174

Explanation:

Evaluating yields –6174.

–147(–21 + 63) =

–147 * 42 = –6174

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Example Question #4 : Algebraic Functions

$f(x)=x^{2}+2$

$g(x)=x-4$

Find $g(f(2))$ .

Possible Answers:

$\dpi{100} \small 3$

$\dpi{100} \small 2$

$\dpi{100} \small 4$

$\dpi{100} \small 1$

$\dpi{100} \small 6$

Correct answer:

$\dpi{100} \small 2$

Explanation:

$g(f(2))$ is $\dpi{100} \small 2$ . To start, we find that $f(2)=2^{2}+2=4+2=6$ . Using this, we find that $g(6)=6-4=2$ .

Alternatively, we can find that $g(f(x))=(x^{2}+2)-4=x^{2}-2$ . Then, we find that $g(f(2))=2^{2}-2=4-2=2$ .

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Example Question #5 : Algebraic Functions

It takes no more than 40 minutes to run a race, but at least 30 minutes. What equation will model this in m minutes?

Possible Answers:

$\left | m-35 \right |= 5$

$\left | m-35 \right |> 5$

$\left | m+35 \right |> 5$

$\left | m-35 \right |< 5$

$\left | m+35 \right |< 5$

Correct answer:

$\left | m-35 \right |< 5$

Explanation:

If we take the mean number of minutes to be 35, then we need an equation which is less than 5 from either side of 35. If we subtract 35 from $m$ minutes and take the absolute value, this will give us our equation since we know that the time it takes to run the marathon is between 30 and 40 minutes.

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GRE Math : How to find f(x)

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 : Algebraic Functions

Example Question #1 : Algebraic Functions

Example Question #2 : Algebraic Functions

Example Question #1 : How To Find F(X)

Example Question #4 : How To Find F(X)

Example Question #3 : Algebraic Functions

Example Question #2 : Algebraic Functions

Example Question #3 : Algebraic Functions

Example Question #4 : Algebraic Functions

Example Question #5 : Algebraic Functions

All GRE Math Resources

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