10.
The functions f and g are defined by
$$\begin{aligned}
& \mathrm { f } ( x ) = 2 ^ { x } , x \in \mathbb { R }
& \mathrm {~g} ( x ) = \sqrt { 1 - x } , x \in \mathbb { R } , x \leq a
\end{aligned}$$
- State the maximum possible value of \(a\).
- The function h is defined by \(\mathrm { h } ( x ) = \mathrm { gf } ( x )\)
- Write down an expression for \(\mathrm { h } ( x )\)
- (ii) Using set notation, state the greatest possible domain of h .
- (iii) State the range of h .