To find the inverse of the given function, solve the equation for f(x) for x, it means, isolate x from the given equation:
[tex]\begin{gathered} f(x)=\sqrt{-3+x} \\ f(x)^2=-3+x \\ f(x)^2+3=x \end{gathered}[/tex]
Now, change f(x) for x and x for f^-1(x):
[tex]f^{-1}(x)=x^2+3[/tex]
According to this, the correct answer is the first choice, this is because the domain of the function has to start at x=0.
The equation of the inverse function is the one shown in the last equation.
f^-1(x)=x²+3
