Question

It’s just apart of a homework practice. When you get the answer, just tell me if the answer is A,B,C,or D.

Answer 1

The function is given as,

$\begin{gathered} f(x)=x^2\text{ - 1} \\ g(x)\text{ = }\sqrt[]{x-3} \end{gathered}$$g(f(x))\text{ is calculated as,}$$\begin{gathered} g(f(x))\text{ = }\sqrt[]{(x^2-1)-3} \\ g(f(x))\text{ = }\sqrt[]{x^2-1-3} \\ g(f(x))\text{ = }\sqrt[]{x^2-4} \end{gathered}$

Thus the required answer is ,

$g(f(x))\text{ = }\sqrt[]{x^2-4}$

The domain of the given function is,

$x\text{ }\leq\text{ }-2\text{ and x }\ge\text{ 2}$

Thus the correct answer is option is (A).