Find the domain of the composite function f $f ^ { \circ } g $
-$$f ( x ) = \sqrt { 2 - x } ; \quad g ( x ) = | 2 x - 1 |$$
A) $\{ x \mid x \leq 2 \}$
B) $\{ x \mid x \geq 2 \}$
C) $\left\{ x \mid - \frac { 1 } { 2 } \leq x \leq \frac { 3 } { 2 } \right\}$
D) all real numbers

Question

Quizplus · Accepted Answer

The domain of $f(g(x))$ is determined by the requirement that $2 - g(x) \geq 0$ because of the square root in $f(x)$, and $g(x) = |2x - 1|$ must be non-negative for all $x$ since it's an absolute value function. To find the domain of $f(g(x))$, we solve $2 - |2x - 1| \geq 0$. This inequality holds for $-\frac{1}{2} \leq x \leq \frac{3}{2}$, which matches option C.

Find the Domain of the Composite Function F f∘gf ^ { \circ } g f∘g

Find the Domain of the Composite Function F $f ^ { \circ } g$