# PSAT Math : Algebraic Functions

## Example Questions

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

If f(x) = x2 – 5 for all values x and f(a) = 4, what is one possible value of a?

8

3

11

14

1

3

Explanation:

Using the defined function, f(a) will produce the same result when substituted for x:

f(a) =  a2 – 5

Setting this equal to 4, you can solve for a:

a2 – 5 = 4

a2 = 9

a = –3 or 3

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

If the function g is defined by g(x) = 4x + 5, then 2g(x) – 3 =

4x + 2

6x + 7

6x + 2

8x + 2

8x + 7

8x + 7

Explanation:

The function g(x) is equal to 4x + 5, and the notation 2g(x) asks us to multiply the entire function by 2. 2(4x + 5) = 8x + 10. We then subtract 3, the second part of the new equation, to get 8x + 7.

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

If f(x) = x2 + 5x and g(x) = 2, what is f(g(4))?

4

14

39

2

36

14

Explanation:

First you must find what g(4) is. The definition of g(x) tells you that the function is always equal to 2, regardless of what “x” is. Plugging 2 into f(x), we get 22 + 5(2) = 14.

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

f(a) = 1/3(a3 +  5a – 15)

Find = 3.

19

1

9

27

3

9

Explanation:

Substitute 3 for all a.

(1/3) * (33 + 5(3) – 15)

(1/3) * (27 + 15 – 15)

(1/3) * (27) = 9

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

Evaluate f(g(6)) given that f(x) = x2 – 6 and g(x) = –(1/2)x – 5

–8

58

–25

30

50

58

Explanation:

Begin by solving g(6) first.

g(6) = –(1/2)(6) – 5

g(6) = –3 – 5

g(6) = –8

We substitute f(–8)

f(–8) = (–8)2 – 6

f(–8) = 64 – 6

f(–8) = 58

### Example Question #6 : How To Find F(X)

If f(x) = |(x– 175)|, what is the value of f(–10) ?

75

–75

15

275

–275

75

Explanation:

If x = –10, then (x2 – 175) = 100 – 175 = –75. But the sign |x| means the absolute value of x. Absolute values are always positive.

|–75| = 75

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

If f(x)= 2x² + 5x – 3, then what is f(–2)?

–1

–5

–21

7

–5

Explanation:

By plugging in –2 for x and evaluating, the answer becomes 8 – 10 – 3 = -5.

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

If f(x) = x² – 2 and g(x) = 3x + 5, what is f(g(x))?

9x² + 30x + 23

9x² + 23

3x² – 1

9x² + 30x + 25

9x² + 30x + 23

Explanation:

To find f(g(x) plug the equation for g(x) into equation f(x) in place of “x” so that you have: f(g(x)) = (3x + 5)² – 2.

Simplify: (3x + 5)(3x + 5) – 2

Use FOIL: 9x² + 30x + 25 – 2 9x² + 30x + 23

### Example Question #9 : How To Find F(X)

f(x) = 2x2 + x – 3 and g(y) = 2y – 7.  What is f(g(4))?

-33

0

57

33

42

0

Explanation:

To evaluate f(g(4)), one must first determine the value of g(4), then plug that into f(x).

g(4) = 2 x 4 – 7 = 1.

f(1) = 2 x 12 + 2 x 1 – 3 = 0.

### Example Question #10 : How To Find F(X)

For all positive integers, let k* be defined by k* = (k-1)(k+2) . Which of the following is equal to 3*+4*?

5*

7*

6*

4* 