Question

If $f\left(x\right)=x+2$, then $f\text{'}\left(f\left(x\right)\right)$ at $x=4$ is

• A. $8$
• B. $1$
• C. $4$
• D. $5$

Answer 1

The correct option is B

$1$

Explanation for the correct option.

Find the value of $f\text{'}\left(f\left(x\right)\right)$ at $x=4$.

For the function $f\left(x\right)=x+2$, the composite function $f\left(f\left(x\right)\right)$ is defined as:

$\begin{array}{rcl}f\left(f\left(x\right)\right)& =& f\left(x+2\right)\\ & =& \left(x+2\right)+2\\ & =& x+4\end{array}$

Now, the derivative of $f\left(f\left(x\right)\right)=x+4$ is given as $f\text{'}\left(f\left(x\right)\right)=1$.

So for all $x$, the value of $f\text{'}\left(f\left(x\right)\right)$ is $1$.

So at $x=4$, the value of $f\text{'}\left(f\left(x\right)\right)$ is $1$.

Hence, the correct option is B.