Question

Need help with the composition of functions. I have attached a screenshot of the question.

Answer 1

So,

To compose a function with another, substitute the inside function into every place where x appears in the outer function.

For (h * h)(x), substitute h(x) for every x in the outer function, h(x).

$h(x)=\frac{6}{x}-->(h^oh)(x)=\frac{6}{\frac{6}{x}}=6*\frac{x}{6}=x$

For (f * f)(x), substitute f(x) for every x in the outer function, f(x).

$f(x)=x^2-5-->(f^of)(x)=(x^2-5)^2-5=x^4-10x^2+20$

Hope this helps!