Question

Given the function

f(x)=4x−1
, evaluate and simplify the expressions below. See special instructions on how to enter your answers.
f(a)=
f(a+h)=
f(a+h)−f(a)h=
Instructions: Simplify answers as much as possible. Expressions such as 4(x+2)and (x+5)2 should be expanded. Also collect like terms, so 3x+x should be written as 4x.

Answer 1

`f(a) = 4a - 1`

`f(a+h) = 4a+4h - 1`

`f(a + h) - f(a)h= 4a + 5h - 4ah- 1`

Explanation:

Given

`f(x) = 4x - 1`

Solving (a): f(a)

Substitute a for x

`f(a) = 4a - 1`

Solving (b): f(a + h)

Substitute a + h for x

`f(a+h) = 4(a+h) - 1`

`f(a+h) = 4a+4h - 1`

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

`f(a + h) - f(a)h= f(a + h) - f(a) * h`

Substitute values for f(a + h) and f(a)

`f(a + h) - f(a)h= 4a + 4h - 1 - (4a- 1) * h`

Open bracket

`f(a + h) - f(a)h= 4a + 4h - 1 - 4ah+ h`

Collect like terms

`f(a + h) - f(a)h= 4a + 4h + h - 4ah- 1`

`f(a + h) - f(a)h= 4a + 5h - 4ah- 1`