Find the Inverse f(x)=cos(x)

Problem

ƒ(x)=cos(x)

Solution

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

y=cos(x)

2. Restrict the domain of the original function to [0,π] so that it is one-to-one and an inverse can exist.

x∈[0,π]

3. Interchange the variables x and y to begin solving for the inverse relationship.

x=cos(y)

4. Solve for y by applying the arccosine function to both sides of the equation.

y=arccos(x)

5. Replace y with the inverse function notation ƒ(x)(−1)

ƒ(x)(−1)=arccos(x)

Final Answer

ƒ(x)(−1)=arccos(x)

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