Question86 FUNCTIONS (Chapter 3) 11 Suppose $f(x)=\sqrt{1-x}$ and $g(x)=x^{2}$. Find: a $(f \circ g)(x)$ b the domain and range of $(f \circ g)(x)$.

Studdy Solution
Determine the range of $(f \circ g)(x) = \sqrt{1 - x^2}$.
The expression $\sqrt{1 - x^2}$ represents the upper half of a circle with radius 1 centered at the origin. The values of $\sqrt{1 - x^2}$ range from 0 to 1 as $x$ varies from $-1$ to $1$.
Thus, the range of $(f \circ g)(x)$ is:
$$[0, 1]$$
The expression for $(f \circ g)(x)$ is $\sqrt{1 - x^2}$, with domain $[-1, 1]$ and range $[0, 1]$.