f(x)=2/3x^2-3/4x+6

Question

Restrict the domain of the function f(x)=2/3x^2-3/4x+6 so that an inverse exists on the restricted domain? What is the restricted domain?

Answer 1

Function

Let us find the inverse of the function to restrict the domain of the function so that

the inverse of the function restricted on domain.

To find the inverse substitute x for y and solve for y.

Multiply each side by 2

So, the inverse of the function is 

.

The domain of this function is

Since in a square root there shouldn't be any negative value

Therefore,

The domain of the function so that inverse exists on this function is .

The restricted domain is all values of x such that