1.1. The function $f(x)$ is defined as

      $f:x↦\sqrt{(25-{x}^{2})}$            $x\inℝ,-5\leqx\leq5$

Explain why the inverse of $f(x)$ does not exist.

1.2. Suggest an adaption to the domain of $f(x)$ so the following conditions are met:

• the inverse of $f(x)$ exists,

• the graph of $y=f(x)$ lies in the first quadrant only, and,

• the domain of $f(x)$ is as large as possible.

State the range for your adapted $f(x)$.

1.3. The domain of $f(x)$is changed to $-5\leqx\leq0.$ 
Find an expression for ${f}^{-1}(x)$ and state its domain and range.