Question

Given the function below, show all the steps to write the equation of the inverse

F(x)= -44rcsin2x

Answer 1

Explanation:

`f(x) = - 44arc \sin(2x)`

`y = - 44 \sin {}^( - 1) (2x)`

Swap x and y.

`x = - 44 \sin {}^( - 1) (2y)`

`- (x)/(44) = \sin {}^( - 1) (2x)`

Take the sin of both sides

`\sin( - (x)/(44) ) = 2y`

`(1)/(2) \sin( - (x)/(44) ) = y`

Let y=f^-1(x)

`f {}^( - 1) (x) = (1)/(2) \sin( - (x)/(44) )`