I have no idea what to do here, can anyone help?:
I have to find the Domain, Range and Inverse.
Domain: Are there any restrictions for x in this expression?
Range: Given the domain, are there any values that y cannot take on?
To find the inverse we must first determine that this is 1 to 1 (which it is.) Then:
Reverse the roles of x and y. (This effectively reflects the function over the line y = x.)
Solve for y:
This is your inverse function.
The situations you need to worry about are functions with vertical asymptotes or that are undefined. For example
is undefined for any values of x that make h(x) = 0. Similarly we can't have any negative numbers or zero in . We also have the case for any "even" radicals that we forbid negative numbers: , or , etc. Since your function contains none of these expressions there is nothing to worry about.
This is slightly more complicated for a non-linear function. For example, using the same domain,
has a range of all real numbers. The best strategy that I have is to graph the function and visually determine the range.