Question

What is the domain and range for the following function and its inverse?

f(x) = x2 + 3

Answer 1

I assume you mean  x^2  + 3. For the function x^2 + 3, the domain is (-infinity,infinity) and the range is (3,infinity). The function's inverse is +- sqrt(-3 + x).

Answer 2

Answer:

Domain of f:R

Range of f:$[3,\infty)$

Domain of inverse of f:$[3,\infty)$

Range of inverse of f:$[0,\infty)$

Step-by-step explanation:

We are given that a function

$f(x)=x^2+3$

Function is defined for every value of x

Therefore, domain of function is R.

Substitute x=0 then we get

$f(0)=3$

Therefore, range of given function is (3,$\infty$).

Suppose, f(x)=y=$x^2+3$

$x=\sqrt{y-3}$

Function is not defined for negative values of x and for 1 and 2.

Therefore, the domain of inverse function of given function is $[3,\infty)$.

When substitute y=3 then we get

x=0

Therefore, the range of given function is $[0,\infty)$