Question

Determine f of the quantity 3 plus h end quantity minus f of 3 all over h if f (x) = 3x − 2.232h3h

Answer 1

The given function f(x) is:

$f(x)=3x-2$

Let's start finding f(4) by replacing x=4:

$\begin{gathered} f(4)=3\cdot4-2 \\ f(4)=12-2 \\ f(4)=10 \end{gathered}$

Now, find f(4+h) by replacing x=4+h:

$\begin{gathered} f(4+h)=3\cdot(4+h)-2 \\ f(4+h)=12+3h-2 \\ f(4+h)=10+3h \end{gathered}$

Thus:

$\begin{gathered} \frac{f(4+h)-f(4)}{h}=\frac{10+3h-10}{h} \\ \Rightarrow\frac{3h}{h} \\ \text{Simplify h/h} \\ \frac{f(4+h)-f(4)}{h}=3 \end{gathered}$

The answer is option b. 3