Chapter 4, Problem 9RE

(a)

To determine

To graph: The function, $f\left(x\right)=x^2-3$ for $x\le 0$.

(b)

To determine

To calculate: If the function defines $f\left(x\right)=x^2-3$ is one-to-one function of $x$.

(c)

To determine

To calculate: The domain of the function $f\left(x\right)=x^2-3$ for $x\le 0$..

(d)

To determine

To calculate: The Range of the function $f\left(x\right)=x^2-3$ for $x\le 0$..

(e)

To determine

To calculate: The equation for an inverse function $f\left(x\right)=x^2-3$.

(f)

To determine

To graph: The graph of $f\left(x\right)=x^2-3$ and $f^{-1}\left(x\right)=-\sqrt{x+3}$.

(g)

To determine

To calculate: Domain of the inverse function $f^{-1}(x)=-\sqrt{x+3}$.

(h)

To determine

To calculate: Range of the inverse function $f^{-1}\left(x\right)=-\sqrt{x+3}$.