# ACT Math : How to find f(x)

## Example Questions

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

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

24

20

18

22

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 : Algebraic Functions

g(x) = 4x – 3

h(x) = .25πx + 5

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

42

π + 17

4

13π + 3

19π – 3

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 #3 : How To Find F(X)

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

(7y+3)/12
(7y+12)/4
(7y+12)/3
(7y-12)/4
Explanation:

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

What is ?

Explanation:

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

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

2x2 + 12x +18

6x2 + 5x

2x2 – 12x +21

6x2 – 12x

2x2

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))?

–132

132

503

128

–503

–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 #1 : Algebraic Functions

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

x3 + 2x2 – x – 8

x3x2x + 8

x3 + 17x2 + 95x + 172

x3 + 2x2 + x + 2

x3 + x2 + 2

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 #1 : How To Find F(X)

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

–6174

3565

2881

–2881

–6174

Explanation:

Evaluating yields –6174.

–147(–21 + 63) =

–147 * 42 = –6174

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

Find .

Explanation:

is . To start, we find that . Using this, we find that .

Alternatively, we can find that . Then, we find that .

### Example Question #1 : 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?