Question

Given the function f ( x ) = 2 x + 8 , evaluate and simplify the expressions below. See special instructions on how to enter your answers.

Answer 1

`f(a) = 2a + 8`

`f(x + h) = 2x + 2h + 8`

`(f(x + h) - f(x))/(h) = 2`

Explanation:

Given

`f(x) = 2x + 8`

Required

`f(a)`

`f(x + h)`

`(f(x + h) - f(x))/(h)`

Solving for f(a)

Substitute a for x in the given parameter

`f(x) = 2x + 8` becomes

`f(a) = 2a + 8`

Solving for f(x+h)

Substitute x + h for x in the given parameter

`f(x + h) = 2(x + h) + 8`

Open Bracket

`f(x + h) = 2x + 2h + 8`

Solving for
`(f(x + h) - f(x))/(h)`

Substitute 2x + 2h + 8 for f(x + h), 2x + 8 fof f(x)

`(f(x + h) - f(x))/(h)` becomes

`(2x + 2h + 8 - (2x + 8))/(h)`

Open Bracket

`(2x + 2h + 8 - 2x - 8)/(h)`

Collect Like Terms

`(2x - 2x+ 2h + 8 - 8)/(h)`

Evaluate the numerator

`(2h)/(h)`

`2`

Hence;

`(f(x + h) - f(x))/(h) = 2`