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Let f(x) = x^2. Find f^−1(x).

User Bhindi
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1 Answer

13 votes

Answer:

Step 1

Substitute f of x with y.

f of x equals x squared. y equals x squared.

Step 2

Switch the x and y variables.

y equals x squared. x equals y squared.

Step 3

Solve for y.

x equals y squared. Square root x equals square root y squared. Don’t forget, when taking the square root of a number or variable, both positive and negative values must be taken into consideration. Plus and minus square root x equals y.

Step 4

Replace y with f inverse x.

Plus and minus square root x equals y. Plus and minus square root x equals f inverse x.

Step 5

Graph the inverse.

A graph of y equals plus and minus square root x. It is a left opening parabola with vertex at point 0 comma 0. If a vertical line were dragged across the graph, that line would cross the graph of y equals plus and minus square root x in more than one place. Therefore, the equation is not a function.

User David Duponchel
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