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

Answer:

$f(a) = 4a - 1$

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

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

Step-by-step 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

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

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