Find the inverse function of F(x)=2 arccos xF^-1(x)=

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03-11-2022
Mathematics

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Find the inverse function of F(x)=2 arccos xF^-1(x)=

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ZymereM104336 ZymereM104336 · Answer 1 · 2022-11-03T14:01:58-04:00

Given the inverse function

[tex]f(x)\text{ = 2arccosx}[/tex]

A function g is the inverse of f if for y = f(x) , x = g(y)

[tex]\begin{gathered} y\text{ = 2arccosx} \\ \arccos x\text{ = }\frac{y}{2} \\ \arccos a\text{ = b} \\ a=\cos (b) \end{gathered}[/tex][tex]\begin{gathered} x=\text{ cos(}\frac{y}{2}) \\ \text{substitute y = x} \\ y=\cos (\frac{x}{2}) \end{gathered}[/tex]

Hence the correct answer is Option B

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