ACT Math : How to find f(x)

Study concepts, example questions & explanations for ACT Math

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Example Questions

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Example Question #82 : Algebraic Functions

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

 

Possible Answers:

20

22

24

18

Correct answer:

24

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.

 

 

 

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

g(x) = 4x – 3

h(x) = .25πx + 5

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

Possible Answers:

π + 17

13π + 3

42

4

19π – 3

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.

Example Question #1 : Algebraic Functions

If 7y = 4x - 12, then x = 

Possible Answers:
(7y+12)/3
(7y-12)/4
(7y+3)/12
(7y+12)/4
Correct answer: (7y+12)/4
Explanation:

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

Example Question #46 : Algebraic Functions

What is ?

Possible Answers:

Correct answer:

Explanation:

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

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

Possible Answers:

6x2 + 5x

2x2  

2x2 + 12x +18

6x2 – 12x

2x2 – 12x +21

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

Example Question #83 : Algebraic Functions

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

Possible Answers:

–503

132

–132

503

128

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.

Example Question #2 : How To Find F(X)

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

Possible Answers:

x3x2x + 8

x3 + 17x2 + 95x + 172

x3 + x2 + 2

x3 + 2x2 + x + 2

x3 + 2x2 – x – 8

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

Example Question #3 : How To Find F(X)

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

Possible Answers:

2881

–6174

–2881

3565

Correct answer:

–6174

Explanation:

Evaluating yields –6174.

–147(–21 + 63) =

–147 * 42 = –6174

Example Question #51 : Algebraic Functions

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

g(x)=x-4

Find g(f(2)).

Possible Answers:

\dpi{100} \small 2

\dpi{100} \small 6

\dpi{100} \small 1

\dpi{100} \small 4

\dpi{100} \small 3

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.

Example Question #5 : How To Find F(X)

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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