Hello.
So, you should already know that to find the inverse of a function you switch x and y and solve.
For f(x) = x² + 3, it's domain is all real numbers, and the range is y ≥ 3.
The inverse of f(x), it is [tex] f^{-1} [/tex], and the equation is [tex] f^{-1} [/tex] = ±√(x - 3). It's domain is x ≥ 3, and the range is all real numbers.
There are many unique characteristics about inverses, like the values of x and y are switched, it's reflected on the line y = x, and the domain and range is switched.
So your final answer is c. f(x) domain: all real numbers, range: y ≥ 3
[tex] f^{-1} [/tex] domain: x ≥ 3, domain: all real numbers.
Hopefully it makes sense! :)
