The actual inverse function is:
[tex]f^{-1}(x) = x^2 + 3[/tex]
And the domain is [0, ∞).
Where is the mistake?
Remember that for a given function f(x) with a domain D and a range R.
For the inverse function, f⁻¹(x) the domain is R and the range is D.
Here, for the given function the domain is x ≥ 3 and the range is [0, ∞).
Then for the inverse function, which is:
[tex]f^{-1}(x) = x^2 + 3[/tex]
(to check this, you must have that):
[tex]f^{-1}(f(x)) = x\\\\f(f^{-1}(x)) = x[/tex]
The domain will be [0, ∞) and the range x ≥ 3
If you want to learn more about inverse functions:
https://brainly.com/question/14391067
#SPJ1
