QuestionFor $f(x)=\sqrt{x}$ and $g(x)=6 x+1$, find the following composite functions and state the domain of each. (a) $f \circ g$ (b) $g \circ f$ (c) $f \circ f$ (d) $g \circ g$

Studdy Solution
Determine the domain of $g \circ g$:
Since $g \circ g$ is a linear function, its domain is all real numbers.
The composite functions and their domains are: (a) $f \circ g(x) = \sqrt{6x + 1}$, domain: $x \geq -\frac{1}{6}$ (b) $g \circ f(x) = 6\sqrt{x} + 1$, domain: $x \geq 0$ (c) $f \circ f(x) = x^{1/4}$, domain: $x \geq 0$ (d) $g \circ g(x) = 36x + 7$, domain: all real numbers