Question

Find and simplify each of the following for f(x) = 7x-9.(A) f(x+h)(B) f(x+h) – f(x)(C) [f(x+h)-f(x)]/h

Answer 1

(a)7x+7h-9

(b)7h

(c)7

Step-by-step explanation:

Given f(x) defined below:

`f\mleft(x\mright)=7x-9`

Part A

`\begin{gathered} f\mleft(x+h\mright)=7(x+h)-9 \\ =7x+7h-9 \end{gathered}`

Part B

`\begin{gathered} f\mleft(x+h\mright)-f\mleft(x\mright)=\lbrack7x+7h-9\rbrack-\lbrack7x-9\rbrack \\ =7x+7h-9-7x+9 \\ =7x-7x+7h-9+9 \\ =7h \end{gathered}`

Part C

Taking the result from Part B:

`\begin{gathered} (f\mleft(x+h\mright)-f\mleft(x\mright))/(h)=(7h)/(h) \\ =7 \end{gathered}`