Question

Find (a) the domain of f and (b) f ^-1 and its domain.

Answer 1

(b)

Step 1:

The function is .

Consider .

Interchange the variables and .

Above function is in the form , where .

The inverse function is .

Step 2:

Solve for .

Apply squaring on both sides.

Apply logarithm on each side.

The inverse function is .

Step 3:

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 .

Solution :

The inverse function is .

The domain of the function is .

Answer 2

(a)

Step 1:

The function is .

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

Since there shouldn't be any negative numbers in the square root.

The expression  should be zero or positive.

Apply logarithm on each side.

The domain of the function is .

Solution :

The domain of the function is .