Answer: [tex]f^{-1}(x)=x^2-3[/tex]
Step-by-step explanation:
Given the function f(x):
[tex]f(x)=\sqrt{x+3}[/tex]
You need to follow these steps in order to find [tex]f^{-1}(x)[/tex]:
- Rewrite the function with [tex]f(x)=y[/tex]:
[tex]y=\sqrt{x+3}[/tex]
- Solve for "x":
[tex](y)^2=(\sqrt{x+3})^2\\\\y^2=x+3\\\\x=y^2-3[/tex]
- Exchange the variables:
[tex]y=x^2-3[/tex]
- Rewrite the function with [tex]y=f^{-1}(x)[/tex]:
[tex]f^{-1}(x)=x^2-3[/tex]
