Question

4. Suppose f(x) = 3x + 4, simplify the following:(a) f(x+h) =(b)f(x+h)-f(x)=

Answer 1

`\begin{gathered} a\text{.} \\ f\mleft(x+h\mright)=3x+3h+4 \\ b\text{.} \\ f\mleft(x+h\mright)-f\mleft(x\mright)=3h \end{gathered}`

Explanation:

We have the following function:

`f\mleft(x\mright)=3x+4`

Now we calculate the following:

(a) f(x+h)

`\begin{gathered} f(x+h)=3\cdot(x+h)+4 \\ f(x+h)=3x+3h+4 \end{gathered}`

(b) f(x+h)-f(x)

`\begin{gathered} f\mleft(x+h\mright)-f\mleft(x\mright)=3\cdot(x+h)+4-(3x+4) \\ f(x+h)-f(x)=3x+3h+4-3x-4 \\ f(x+h)-f(x)=3h \end{gathered}`