Find the Inverse f(x)=x^2

Problem

ƒ(x)=x2

Solution

1. Replace ƒ(x) with y to represent the dependent variable.

y=x2

2. Interchange the variables x and y to begin finding the inverse relationship.

x=y2

3. Solve for y by taking the square root of both sides of the equation.

y=±√(,x)

4. Restrict the domain if necessary. Since the original function ƒ(x)=x2 is not one-to-one over all real numbers, its inverse is typically defined for the principal branch where x≥0

ƒ(x)(−1)=√(,x)

Final Answer

ƒ(x)(−1)=√(,x)

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