Answered

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If f(x) =[tex]\sqrt{x} +3[/tex] , what is the equation for f–1(x)?

Sagot :

razorsharptip

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]

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