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 #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:

18

24

22

20

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)

If f(x) = 3x2 + 6x + 27, then f (-1)=?

 

Possible Answers:

24

-36

18

36

Correct answer:

24

Explanation:

To solve this question, you substitute -1 for x. You should get, f(-1)= 3 + (-6) +27= 24. If you didn’t remember the negative sign, you would get 36. If you remembered the negative sign at the very last step, you would get -36. If you didn’t remember that (-1)2 is +1, then you would get 18.

 

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:

19π – 3

π + 17

42

13π + 3

4

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 : How To Find F(X)

If 7y = 4x - 12, then x = 

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

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

Example Question #190 : Algebraic Functions

What is ?

Possible Answers:

Correct answer:

Explanation:

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

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

Possible Answers:

2x2 – 12x +21

2x2 + 12x +18

6x2 + 5x

6x2 – 12x

2x2  

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 #1 : How To Find F(X)

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 #4 : How To Find F(X)

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

Possible Answers:

x3 + 2x2 – x – 8

x3 + 17x2 + 95x + 172

x3x2x + 8

x3 + 2x2 + x + 2

x3 + x2 + 2

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 #45 : How To Find F(X)

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

Possible Answers:

–2881

2881

3565

–6174

Correct answer:

–6174

Explanation:

Evaluating yields –6174.

–147(–21 + 63) =

–147 * 42 = –6174

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

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

g(x)=x-4

Find g(f(2)).

Possible Answers:

\dpi{100} \small 2

\dpi{100} \small 3

\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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