Chapter 4.1, Problem 61PE

(a)

To determine

To Graph: The equation $f(x)=\sqrt{x+1}$

(b)

To determine

Is $f(x)=\sqrt{x+1}$ is one-to-one function

(c)

To determine

Domain of function $f(x)=\sqrt{x+1}$ in interval notation.

(d)

To determine

Range of function $f(x)=\sqrt{x+1}$ in interval notation.

(e)

To determine

The inverse function of equation $f(x)=\sqrt{x+1}$, That is $f^{-1}(x)$.

(f)

To determine

Why the restriction $x\ge 0$ is placed on $f^{-1}$.

(g)

To determine

To Graph: Graph $y=f(x)$ and $y=f^{-1}(x)$ on the same co-ordinate system that is $f(x)=\sqrt{x+1}$ and $f^{-1}(x)=x^2-1;x\ge 0$

(h)

To determine

Domain of $f^{-1}(x)=x^2-1;x\ge 0$ in interval notation.

(h)

To determine

Range of $f^{-1}(x)=x^2-1;x\ge 0$ in interval notation.