$\"\"$

\

The functions is $\"\"$ and inverse function is $\"\"$ .

\

(a)

\

Find the domain of $\"image\"$ and $\"image\"$ .

\

The cubic polynomial function $\"\"$ is increasing function.

\

The domain of a function is all possible $\"image\"$ -values.

\

Domain of a polynomial function is always all real numbers.

\

Domain of $\"image\"$ is $\"\"$ .

\

Domain of cube root function is all real numbers.

\

Domain of $\"image\"$ is $\"\"$ . $\"\"$

\

(b)

\

Find the range of $\"image\"$ and $\"image\"$ .

\

The Domain of $\"image\"$ is equal to the range of $\"image\"$ and the range of $\"image\"$ is equal to the domain of $\"image\"$ .

\

Range of $\"image\"$ is $\"\"$ .

\

Range of $\"image\"$ is $\"\"$ .

\

$\"\"$

\

(c)

\

Graph the two functions $\"image\"$ and inverse function is $\"\"$ .

\

Graph:

\

$\"\"$

\

\

$\"\"$

\

(d)

\

The functions are $\"\"$ and $\"\"$ .

\

First derivative is slope of the function.

\

Find the slopes of the $\"\"$ and $\"\"$ at the given points.

\

$\"\"$

\

$\"\"$

\

The point is $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

The point is $\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

The slopes of the $\"image\"$ and $\"image\"$ are reciprocal at the points $\"\"$ , $\"\"$ .

\

Graph:

\

$\"\"$

\

$\"\"$

\

(a)

\

Domain of $\"image\"$ is $\"image\"$ and domain of $\"image\"$ is $\"image\"$ .

\

(b)

\

Range of $\"image\"$ is $\"image\"$ and range of $\"image\"$ is $\"image\"$ .

\

(c)

\

$\"\"$

\

(d) The slopes of the $\"image\"$ and $\"image\"$ are reciprocal at the points $\"\"$ , $\"\"$ .