Question

Please help I need by Tomorrow!

Answer 1

`f(a) = 5a + 1`

`f(a + h) = 5a + 5h +1`

`(f(a + h) - f(a))/(h) =5`

Explanation:

Given

`f(x) = 5x + 1`

Solving (a): f(a)

Substitute a for x in
`f(x) = 5x + 1`

`f(a) = 5a + 1`

Solving (b): f(a + h)

Substitute a + h for x in
`f(x) = 5x + 1`

`f(a + h) = 5(a + h) +1`

Open bracket

`f(a + h) = 5a + 5h +1`

Solving (c):
`(f(a + h) - f(a))/(h)`

In (a):

`f(a) = 5a + 1`

In (b):

`f(a + h) = 5a + 5h +1`

So:

`(f(a + h) - f(a))/(h) =(5a+5h+1 - (5a+1))/(h)`

Open bracket

`(f(a + h) - f(a))/(h) =(5a+5h+1 - 5a-1)/(h)`

Collect Like Terms

`(f(a + h) - f(a))/(h) =(5a- 5a+5h+1 -1)/(h)`

`(f(a + h) - f(a))/(h) =(5h)/(h)`

`(f(a + h) - f(a))/(h) =5`