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**FUNCTIONS**

*function*is a mathematical expression, usually denoted by f(x) which read as the function of x

*.*The "f(x)" with "x" is the input for the output to behave of what certain value will be replaced to "x" as input. Let say, the function equation f(x) = 3x-1. The "x" in f(x) should be replaced by any number as an input. By illustration, let x=2, then the

*f(x) = 3x-1*

*will now became*

*f(2) = 3*2-1.*The 3x-1 in f(x) = 3x-1, will at the same time behaved with f(x). Now, executing the relationship of f(x) = 3x-1 with respect to the value of x as 2, then

*f(2) = 3*2-1 =6-1 = 5.*Thus f(2) = 5.

**More illustrative examples:**

1. Given that

*:*

**f(x) = 2x +1****Evaluate:**

a).

*f(1)*

b.

*f(-1)*

c) f

*(-3)*

**Solution for:****a) f(x) = 2x +1;**

*@ x=1*

*f (1) =2*1+1*

f (1) = 2 + 1

f (1) = 3

*answer*

b). f(x) = 2x +1;

*@ x=-1*

*f(-1) =2(-1)+1*

f(-1) = -2 + 1

f(-1) = -1

*answer*

c). f(x) = 2x +1;

*@ x=-3*

*f(-3) =2(-3)+1*

f(-3) = -6 + 1

f(-3) = -5

*answer*

*2). Given that g(x) = 3x -2:*

Evaluate:

a). g(0)

b. g(-2)

c) g(3)

Solution for:

a). g(x) = 3x -2;

*@ x =0*

g(0) = 3(0) - 2

g(0) = 0 - 2

g(0) = -2

*answer*
b). g(x) = 3x -2;

*@ x =-2*

g(-2) = 3(-2) -2

g(-2) = -6 - 2

g(-2) = -8

*answer*
c). g(x) = 3x -2;

*@ x =3*

g(-3) = 3(-3) -2

g(-3) = -9 - 2

g (-3) = -11

*answer***Exercises. Evaluate each given functions:**

Given:

Let: A) f (x) = x

^{2}– 3x + 2,

B) g (x) = 2x

^{2}+ 3x - 1,

C) h (x) = x

^{2}– 3;

**Evaluate:**

1. f (-2) = ___________

2. g (-1) = ___________

3. f ( 0 ) = ___________

4. g (2a) = ___________

5. f - c) = ___________

6. h (2z) = ___________

7. f (- a b) = __________

8. f [ h (-2) ] = ________

9. g [ f (2a) ] = ________

10. f { g [ h (-2) ] } = _________

*(Please comment for improvement. thank you)*