Question

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

Answer 1

Answer:

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

Step-by-step explanation:

$\displaystyle y=\frac{cos^{-1} (\pi x)}{2} -3$

Swicth variables.

$\displaystyle x=\frac{cos^{-1} (\pi y)}{2} -3$

Solve for y.

Add 3 to both sides.

$\displaystyle x+3=\frac{cos^{-1} (\pi y)}{2}$

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 $\pi$.

$\displaystyle \frac{cos(2x+6)}{\pi} =y$

Answer 2

Answer:

$f^{-1}(x) = \frac{cos(2x+6)}{\pi }$

Step-by-step explanation:

$y = \frac{1}{2} cos^{-1} (\pi x)-3$

Firstly, we've to interchange the variables.

$x = \frac{1}{2} cos^{-1}(\pi y)-3$

Solving for y

$x = \frac{cos^{-1} \pi y}{2} -3$

Adding 3 to both sides

$x+3 = \frac{cos^{-1}(\pi y)}{2}$

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

$y = \frac{cos(2x+6)}{\pi }$

Replace y by $f^{-1}(x)$

=> $f^{-1}(x) = \frac{cos(2x+6)}{\pi }$