Question

Using composition of functions, determine if the two functions are inversesof each other.F(x)=√x+4, x ≥ 0G(x)=x²-4, x2227OA. No, because the composition does not result in an answer of x.OB. Yes, because the composition results in an answer of x for x ≥ 2.OC. Yes, because F(x) is equal to -G(x).OD. No, because the functions contain different operations.SUBMIT

Answer 1

Composition of inverse functions:

$\begin{gathered} f(f(x))=x,\text{ for all x in the domain of g} \\ g(f(x))=x,\text{ for all x in the domain of f} \end{gathered}$

For the given functions:

$\begin{gathered} F(x)=\sqrt{x}+4 \\ G(x)=x^2-4 \\ \\ F(G(x))=\sqrt{x^2-4}+4=\sqrt{(x+2)(x-2)}+4 \\ G(F(x))=(\sqrt{x}+4)\placeholder{⬚}^2-4=x+8\sqrt{x}+16-4=x+8\sqrt{x}+12 \end{gathered}$

As you can see above the compossition of the given functions is not equal to x, then the given functions are not inverse

Answer: A. No, because the composition does not result in an answer of x.