Question

PLEASE HURRY write the equation of the inverse function y=1/2cos^-1(pix)-3

Answer 1

`\large \boxed{f^(-1)(x)=(cos(2x+6))/(\pi) }`

Explanation:

`\displaystyle y=(cos^(-1) (\pi x))/(2) -3`

Swicth variables.

`\displaystyle x=(cos^(-1) (\pi y))/(2) -3`

Solve for y.

Add 3 to both sides.

`\displaystyle x+3=(cos^(-1) (\pi y))/(2)`

Multiply both sides by 2.

`\displaystyle 2(x+3)=cos^(-1) (\pi y)`

`\displaystyle 2x+6=cos^(-1) (\pi y)`

Take the cos of both sides.

`\displaystyle cos(2x+6)=\pi y`

Divide both sides by
`\pi`.

`\displaystyle (cos(2x+6))/(\pi) =y`

Answer 2

`f^(-1)(x) = (cos(2x+6))/(\pi )`

Explanation:

`y = (1)/(2) cos^(-1) (\pi x)-3`

Firstly, we've to interchange the variables.

`x = (1)/(2) cos^(-1)(\pi y)-3`

Solving for y

`x = (cos^(-1) \pi y)/(2) -3`

Adding 3 to both sides

`x+3 = (cos^(-1)(\pi y))/(2)`

Multiplying 2 to both sides

`2(x+3) = cos^(-1) (\pi y)\\2x+6 = cos^(-1) (\pi y)`

Taking cosine on both sides

`\pi y = cos (2x+6)`

Dividing both sides by y

`y = (cos(2x+6))/(\pi )`

Replace y by
`f^(-1)(x)`

=>
`f^(-1)(x) = (cos(2x+6))/(\pi )`