Question

let f(x)=sqr of x, g(x)=1/x-4 and h(x)= sqr of 5-x
determine when the following functions are continuous.
a) (fog)(x)
b) (gof)(x)

Answer 1

\(\bf f(x) = \sqrt{x}\qquad g(x) = \cfrac{1}{x-4}\qquad h(x)= \sqrt{5-x}\\\quad \\
(fog)(x) \implies f(\quad g(x)\quad )\implies \sqrt{\left(\cfrac{1}{x-4}\right)} \implies \cfrac{\sqrt{1}}{\sqrt{x-4}}
\\\quad \\

(gof)(x) \implies g(\quad f(x)\quad )\implies \cfrac{1}{\left(\sqrt{x}\right)-4}\)