Question

assume that ( h
eq 0 ). for the function ( f(x)=3x - 3 ), find and simplify: ( \frac{f(x + h)-f(x)}{h} )

Explanation:

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

Substitute \( x+h \) into \( f(x)=3x - 3 \).
\( f(x + h)=3(x + h)-3=3x+3h - 3 \)

Step2: Substitute \( f(x + h) \) and \( f(x) \) into the formula

\(\frac{f(x + h)-f(x)}{h}=\frac{(3x + 3h-3)-(3x - 3)}{h}\)
Simplify the numerator: \((3x + 3h-3)-(3x - 3)=3x+3h - 3-3x + 3=3h\)
So the expression becomes \(\frac{3h}{h}\)

Step3: Simplify the fraction

Since \(h
eq0\), \(\frac{3h}{h}=3\)

Answer:

\(3\)