Question

Find the inverse of the function f(x) = 5 – sqrt(2x – 3). State Domain and range of the inverse.

Answer 1

Step 1:

The function is .

Find inverse of the function .

.

Change  to .

.

Interchange  and .

.

Solve for .

Square on both sides.

Change  to .

.

Step 2 :

Find the domain and range of inverse function.

.

.

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

As the inverse function is a polynomial, domain of a function is all real numbers.

Restrictions over domain :

The domain of  is the range of .

Range of the function is  is .

Domain of  is .

Range of  function is corresponding values of the function for different values of .

.

Outcome of the above function is always positive since it contains squared term.

Thus, the range of the inverse function is .

Solution:

Inverse of the function is .

Domain of  is .

Range of the inverse function is .