The function f(x)=(x-1)^2-4 is not one-to-one. if you restrict the domain for f(x) to x(less than or equal to symbol)1, what is its inverse function and the domain for the inverse?

The function f(x) is given by:

The domain is restricted to x≤1

so that the function is one-one.

Also, the range of  function is:

Now, as the function is one-one and it is onto as well.

Hence, the inverse of the function exist and it is a function as well.

and we find the inverse function as follows:

Keep f(x)=y

interchange x and y

Now we solve for y

Hence, the inverse function is:

and the domain of inverse function is the range of the function.

Hence the domain is:

step-by-step explanation:

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .