Question

If $f\left(x\right)=x^2$, $-1\le x\le 4$ ,$g\left(x\right)=se{c}^{-1}x$, $x\ge 1$ then

• A. Domain of gof(x) is $[1,4]\cup -1$
• B. Domain of gof(x) is $[1,4]$
• C. Range of gof(x) is $[0,se{c}^{-1}16]$
• D. Range of fog(x) is $(0,\frac{{\pi }^2}{4})$

Answer 1

Answer: (A), (C)

Domain of gof(x) is $[1,4]\cup -1$
Range of gof(x) is $[0,se{c}^{-1}16]$

gof(x) exists when $f\left(x\right)\ge 1$ and $xϵ[-1,4]$
$x^2\ge 1\Rightarrow Xϵ(-\infty ,-1]\cup [1,\infty )$
$\Rightarrow Xϵ[1,4]\cup -1$
Range of $gof\left(x\right)=[0,se{c}^{-1}16]$