Q. If $f(x) = x^{2} - 1$ and $g(x) = (x + 1)^{2}$, then $(gof)(x)$ is
A) $(x + 1)^{4} - 1$
B) $x^{4} - 1$
C) $x^{4}$
D) $(x + 1)^{4}$
Explanation
(c)
$gof(x) = g\{ f(x)\}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = g\left( x^{2} - 1 \right) = \left( x^{2} - 1 + 1 \right)^{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = x^{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.