Question

what function is the inverse of f(x)= x^2 +3

f^-1(x)=sqrtx-3
f^-1(x)=sqrt(x)-3
f^-1(x)=x^2-3
f^-1(x)=sqrt(x+3)

Answer 1

None of the four choices is correct.

Solve y = x^2 + 3 for x: x^2 = y − 3, so x = ±√(y − 3). Writing y as the input x for the inverse gives
f⁻¹(x) = ±√(x − 3).

If you need a single-valued inverse function, restrict the domain of f:
- For f restricted to x ≥ 0, f⁻¹(x) = √(x − 3), domain x ≥ 3.
- For f restricted to x ≤ 0, f⁻¹(x) = −√(x − 3), domain x ≥ 3.