__Objectives__

At the end of the lesson, students should be able to;

- Use notation to describe simple functions.
- Find the value of the function at some point.
- Write down an expression for the function when given different values of x.
- Find the value of x, when two functions are equal
- Find the value of x, when given the equivalent value of the function.

An expression in the form **3x – 2**, in which the variable is **x** is considered “**a function of x**”. The numerical value of the expression depends on the value of **x**. This expression can also be written as

__Example 1__

If **f(x) = 4x + 2**, find the value of **f (2)** and **f (-3).**

__Solution__

We use simple substitution of **x** for the values **2** and **-3.**

**f (2)** implies that the value of **x** is given as **2**. We substitute the value of** x** into the expression** f (x)= 4x + 2** to find the corresponding output.

f(x) = 4x + 2

f(2) = 4(2) + 2

= 8 + 2

= 10

Substituting **-3** into the expression will give us the result below.

f (-3) = 4(-3) + 2

= -12 + 2

= –10

__Example 2__

If **f(x) = 5 – 2x**, find the value of **f (3)** and **f (-3).**

__Solution__

Substitute **3** into the expression.

**f (x) = 5 – 2x**

f (3) = 5 – 2(**3**)

= 5 – 6

= -1

Substitute -3 into the expression f(x)= 5-2x.

f (-3) = 5 – 2 (-3)

= 5 + 6

= 11

__Example 5__

There are instances where numbers are not given for substitution but instead algebraic expressions.

If f(x) = x + 2, simplify

1) f ( 2x+5)

2) f ( x ) – 4x

3) f( ^{3}/_{2} x + 10 )

__Example 6__

There are instances where you will be asked to solve a linear equation.

If f(x) = 6x +16 and f(x) =10, solve for x.

__Solution__

f(x) = 6x + 16 and f(x) = 10

Substitute f(x) =10 into f(x) = 6x + 16

10 = 6x + 16

10 – 16 = 6x

– 6 = 6x

x=-1

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