Question

given $f(x)=4x - 7$,
(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 \( f(x)=4x - 7 \).
\( f(x + h)=4(x + h)-7 \)
Expand the expression: \( f(x + h)=4x+4h - 7 \)

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

First, \( f(x + h)=4x + 4h-7 \) and \( f(x)=4x - 7 \)
Then \( f(x + h)-f(x)=(4x + 4h-7)-(4x - 7) \)
Simplify the numerator: \( 4x + 4h-7 - 4x + 7=4h \)
So \( \frac{f(x + h)-f(x)}{h}=\frac{4h}{h} \)
Cancel out \( h \) (assuming \( h
eq0 \)): \( \frac{4h}{h}=4 \)

Answer:

(a) \( f(x + h)=4x + 4h-7 \)
(b) \( \frac{f(x + h)-f(x)}{h}=4 \)