QuestionFind the compositions of the functions: (a) $(f \circ g)(x)$, (b) $(g \circ f)(x)$, (c) $(f \circ f)(x)$, (d) $(g \circ g)(x)$, where $f(x)=x^{2}-4 x$ and $g(x)=x-4$.

Studdy Solution
implify the expression.
$$(g \circ g)(x) = x -8$$So, the solutions are(a) $(f \circ g)(x) = x^{2} -12x +32$ (b) $(g \circ f)(x) = x^{2} -4x -4$ (c) $(f \circ f)(x) = x^{4} -16x^{3} +60x^{2} +16x$ (d) $(g \circ g)(x) = x -8$