1. ## The inverse function

Hey guys, was just wondering if you could help me solve an understanding issue. Was just curious if i had the function sin10x, with a restricted domain (obviously), would the inverse function be (1/10)sin-1x? I done this by simply swapping the x and y values and then rearranging the equation. If i am wrong please show me the correct working.

Hey guys, was just wondering if you could help me solve an understanding issue. Was just curious if i had the function sin10x, with a restricted domain (obviously), would the inverse function be (1/10)sin-1x? I done this by simply swapping the x and y values and then rearranging the equation. If i am wrong please show me the correct working.
sin(10x) = y

10x = arcsin(y)

x = (0,1)(arcsin(y))

Swap x and y

y = (0,1)(arcsin(x))

Note the domain of f equals the range of inverse f ; and the range of f equals the domain of inverse f. (y = f(x))

3. Okay but when i sketch, y = .1arcsinx and y = sin10x, im not getting that inverse reflection look when insert y = x. Why is this?