Question

How do i solve this question

Answer 1

`\bf \begin{cases} h(x)=(f\circ g)(x)\\ h(x)=√(x+5)\\ f(x)=√(x+2) \end{cases}\\\\ -------------------------------\\\\ (f\circ g)(x)\implies f[\ g(x)\ ]\implies f[\ g(x)\ ]=√(g(x)+2)\qquad thus \\\\\\ √(g(x)+2)=(f\circ g)(x)=h(x)=√(x+5)\qquad therefore \\\\\\ √(g(x)+2)=√(x+5)\impliedby \textit{squaring both sides}\\\\\\ g(x)+2=x+5\implies g(x)=x+5-2\implies \boxed{g(x)=x+3}`