Find the inverse function of F(x) = 2arccosx. F-1(x) = ____ a.) 1/2 cos(x) b.) 2 cos(x) c.) cos (1/2 x) d.) cos (2x)

Question

Find the inverse function of F(x) = 2arccosx. F-1(x) = ____
a.) 1/2 cos(x)
b.) 2 cos(x)
c.) cos (1/2 x)
d.) cos (2x)

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Everleigh 2 weeks 2021-10-13T23:38:41+00:00 1 Answer 0

Answers ( )

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    2021-10-13T23:39:44+00:00

    ANSWER

    C.

    {f}^{ - 1} (x) =  \cos( \frac{x}{2} )

    EXPLANATION

    The given function is

    f(x) = 2 \arccos(x)

    Let

    y= 2 \arccos(x)

    Interchange x and y.

    x= 2 \arccos(y)

    Divide both sides by 2.

     \frac{x}{2}  = \arccos(y)

    We take cosines to get,

     \cos( \frac{x}{2} )  = y

     {f}^{ - 1} (x) =  \cos( \frac{x}{2} )

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