Question

Consider the function and its inverse.

Answer 1

Answer:

The domain of $f(x)$ is restricted to $x\leq 0$, and the domain of $f^{-1}(x)$ is restricted to $x\geq 4$.

Step-by-step explanation:

From Function Theory we know that domain of a function is the set of values such that an image exist. Let $f(x) = x^{2}+4$ and $f^{-1}(x) = \sqrt{x-4}$ the function and its inverse, respectively.

At first glance we notice that function is a second order polynomial and every polinomial is a continuous function and therefore, there exists an image for every element of domain.

But domain of its inverse is restricted to every value of x so that $x-4 \geq 0$, which means that $x\geq 4$.

Finally, we concluded that following answer offers the best approximation to our result:

The domain of $f(x)$ is restricted to $x\leq 0$, and the domain of $f^{-1}(x)$ is restricted to $x\geq 4$.