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

Question

asked Jul 11, 2023 21.8k views

1 Answer

Abhay Gupta · Answer 1 · 2023-07-16T18:40:32+0000

The given function f(x) is:

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:

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

The answer is option b. 3