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Answer: [tex]f^{-1}(x) = (x-3)^2[/tex]
Step-by-step explanation:
We are given that [tex]f(x) = \sqrt{x} + 3[/tex]. A trick to solve for the inverse is to switch the f(x) and x in the equation. This gives us
[tex]x = \sqrt{f(x)} + 3[/tex]
Now, we can solve for this f(x) which gives us
[tex]x = \sqrt{f(x)} + 3\\x -3 = \sqrt{f(x)}\\(x -3)^2 = f(x)[/tex]
Then we simply let that [tex]f(x)[/tex] be [tex]f^{-1}(x)[/tex]. Thus, we have [tex]f^{-1}(x) = (x-3)^2[/tex]