Answer:
[tex]f^{-1} (x)=x^{2} -3[/tex]
Step-by-step explanation:
Given the function
[tex]f\left(x\right)=\sqrt{x+3}[/tex]
We can find the inverse function by exchanging x and y, and then solve for y.
[tex]y=\sqrt{x+3}[/tex]
Replace x with y.
[tex]x=\sqrt{y+3}[/tex]
square both sides
[tex]x^2=y+3[/tex]
[tex]y=x^2-3[/tex]
Hence,
[tex]f^{-1} (x)=x^{2} -3[/tex]
