Question

given ( f(x)=9x + 4 ),
(a) find ( f(x + h) ) and simplify.
(b) find ( \frac{f(x + h)-f(x)}{h} ) and simplify.
part: ( 0 / 2 )
part 1 of 2
(a) ( f(x + h)= )

Explanation:

Step1: Find \( f(x + h) \)

Substitute \( x+h \) into \( f(x)=9x + 4 \).
\( f(x + h)=9(x + h)+4 \)
Expand the expression: \( f(x + h)=9x+9h + 4 \)

Step2: Find \( \frac{f(x + h)-f(x)}{h} \)

First, substitute \( f(x + h)=9x+9h + 4 \) and \( f(x)=9x + 4 \) into \( \frac{f(x + h)-f(x)}{h} \).

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Cancel out \( h \) (assuming \( h
eq0 \)): \( \frac{9h}{h}=9 \)

Answer:

(a) \( f(x + h)=9x + 9h+4 \)
(b) \( \frac{f(x + h)-f(x)}{h}=9 \)