Question

Will someone explain what i did wrong here?

Answer 1

The actual inverse function is:

$f^{-1}(x) = x^2 + 3$

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:

$f^{-1}(x) = x^2 + 3$

(to check this, you must have that):

$f^{-1}(f(x)) = x\\\\f(f^{-1}(x)) = x$

The domain will be [0, ∞) and the range x ≥ 3

If you want to learn more about inverse functions:

brainly.com/question/14391067

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