Find the Inverse Function F(x)=cos(x)

$F (x) = \cos (x)$

Replace $F (x)$ with $y$ .

$y = \cos (x)$

Interchange the variables.

$x = \cos (y)$

Solve for $y$ .

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Rewrite the equation as $\cos (y) = x$ .

$\cos (y) = x$

Take the inverse cosine of both sides of the equation to extract $y$ from inside the cosine.

$y = \arccos (x)$

Remove parentheses.

$y = \arccos (x)$

Solve for $y$ and replace with $F^{- 1} (x)$ .

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Replace the $y$ with $F^{- 1} (x)$ to show the final answer.

$F^{- 1} (x) = \arccos (x)$

Set up the composite result function.

$g (F (x))$

Evaluate $g (F (x))$ by substituting in the value of $F$ into $g$ .

$g (\cos (x)) = \arccos (\cos (x))$

Since $g (F (x)) = x$ , $F^{- 1} (x) = \arccos (x)$ is the inverse of $F (x) = \cos (x)$ .

$F^{- 1} (x) = \arccos (x)$

Find the Inverse Function F(x)=cos(x)

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