Question

If f(x) = -x² - 1, and
g(x) = x+5, then
g(f(x)) = ? x²
+

Answer 1

`\begin{cases} f(x)=-x^2-1\\\\ g(x)=x+5 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ g( ~~ f(x) ~~ )=[ ~~ f(x) ~~ ]+5\implies g( ~~ f(x) ~~ )=[ ~~ \underset{f(x)}{-x^2-1} ~~ ]+5 \\\\\\ g( ~~ f(x) ~~ )=-x^2-1+5\implies g( ~~ f(x) ~~ )=-x^2+4`