$\"\"$

\

(a)

\

The function is $\"\"$ .

\

The domain of a function is all values of x, those makes the function mathematically correct.

\

Since there should not be any negative numbers in the square root.

\

The expression $\"\"$ should be zero or positive.

\

$\"\"$

\

Apply logarithm on each side.

\

$\"\"$

\

Therefore,the domain of the function is $\"\"$ .

\

$\"\"$

\

(b)

\

The function is $\"\"$ .

\

Consider $\"\"$ , then $\"\"$ .

\

$\"\"$

\

Take square root on each side.

\

$\"\"$

\

$\"\"$

\

Take natural logarithm on each side.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Interchange $\"image\"$ and $\"image\"$ .

\

$\"\"$

\

Therefore, $\"\"$ .

\

The inverse function is $\"\"$ .

\

$\"\"$

\

The inverse function is $\"\"$ .

\

The domain of a function is all values of x, those makes the function mathematically correct.

\

Since there should not be any negative numbers and zero in the logarithm function.

\

The expression $\"\"$ should be positive.

\

$\"\"$

\

The domain of the inverse function is $\"\"$ .

\

$\"\"$

\

(a) The domain of the function is $\"\"$ .

\

(b) The inverse function is $\"\"$ .

\

The domain of the inverse function is $\"\"$ .