Question

Determine whether the function is one - to - one. if it is, find its inverse function.

f (x) = √(x - 2)

Answer 1

Step 1:

The function is .

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

is never be negative number.

The domain of function is .

The range of function is .

The function is increasing on entire its domain.

The function is .

Apply derivative on each side with respect to .

.

The domain of is .

  is positive on the domain of .

The function is one to one function.

Step 2:

The function is .

Change to .

Interchange and .

Solve for .

Change to .

.

Solution:

The function is one to one.

.