Question

If $f\left(x\right)=x^2-1$ and $g\left(x\right)={\left(x+1\right)}^2$, then $\left(gof\right)\left(x\right)$ is equal to

• A. ${\left(x+4\right)}^4-1$
• B. $x^4-1$
• C. $x^4$
• D. ${\left(x+1\right)}^4$
• E. ${\left(x-1\right)}^4-1$

Answer 1

The correct option is C

$x^4$

Explanation for the correct option:

Finding the value of $\left(gof\right)\left(x\right)$:

Given that,

$f\left(x\right)=x^2-1$

$g\left(x\right)={\left(x+1\right)}^2$

Now,

$\begin{array}{rcl}\left(gof\right)\left(x\right)& =& g\left(f\left(x\right)\right)\\ & =& g\left(x^2-1\right)\\ & =& {\left(x^2-1+1\right)}^2\\ & =& x^4\end{array}$

Hence, the correct option is C.