Question

Given f(x) = 9x-9,

(a) Find f(x+h) and simplify.

(b) Find f(x+h)-f(x)/h
and simplify.

Answer 1

`(a) \(f(x+h) = 9x + 9h - 9\).`

`(b) \((f(x+h) - f(x))/(h) = 9\).`

Let's solve each part step by step:

(a) Find
`\( f(x+h) \)` and simplify:

`\[ f(x+h) = 9(x+h) - 9 \]`

Distribute the 9:

`\[ f(x+h) = 9x + 9h - 9 \]`

Combine like terms:

`\[ f(x+h) = 9x + 9h - 9 \]`

(b) Find
`\( (f(x+h) - f(x))/(h) \)` and simplify:

`\[ (f(x+h) - f(x))/(h) = ((9x + 9h - 9) - (9x - 9))/(h) \]`

Expand and simplify the numerator:

`\[ (9x + 9h - 9 - 9x + 9)/(h) \]`

Combine like terms in the numerator:

`\[ (9h)/(h) \]`

Cancel the common factor of h:

`\[ 9 \]`

`\( (f(x+h) - f(x))/(h) = 9 \).`