assume that ( h \neq 0 ). for the function ( f(x)=3x - 3 ), find and simplify: ( \frac{f(x + h)-f(x)}{h} )
assume that ( h \neq 0 ). for the function ( f(x)=3x - 3 ), find and simplify: ( \frac{f(x + h)-f(x)}{h} )
Answer
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\neq0), (\frac{3h}{h}=3)
Answer:
(3)