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Let f(x) = √x-5

Find f^ -1.

1 Answer

6 votes

Answer:


f^(-1)(x)= x^2 + 5 \,,\,\,x\geq 0

Explanation:

Use the method of swapping x and y and isolating y.


f(x) = y = √(x-5)\,,\,\,\,x\geq 5,y\geq0\\\\f^(-1):x=√(y-5)\,,\,\,\,y\geq 5, x\geq 0\\x^2 = y-5\\y = x^2 + 5 = f^(-1)(x)\\

Note that domain/range will be swapped as well.

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