Composition of Functions

Consider the functions $f(x) = \frac{1}{x-a}$ and $g(x) = \sqrt{x}$, where $a$ is a real number. Analyse the conditions on $a$ for which the…

Let $f(x) = x + 2$ and $g(x) = x^2 - 1$. Define the composite function $f(g(x))$ and state its rule.

Let $f(x) = \frac{1}{x-2}$ and $g(x) = \sqrt{x+1}$. Explain why the composite function $f(g(x))$ is defined, but $g(f(x))$ is not defined fo…