Question

Use f(x) = 2x − 5 and g(x) = 3 − x2
to evaluate the expression (g o g)(x)

Answer 1

\[\large g(x) = 3-x^2\]



\[\large g(g(x)) = 3-(g(x))^2\]


\[\large g(g(x)) = 3-(3-x^2)^2\]


\[\large g(g(x)) = 3-(3-x^2)(3-x^2)\]


\[\large g(g(x)) = 3-(9-3x^2-3x^2+x^4)\]


\[\large g(g(x)) = 3-(9-6x^2+x^4)\]


\[\large g(g(x)) = 3-9+6x^2-x^4\]


\[\large g(g(x)) = -x^4+6x^2-6\]