A function is a **mapping**, you plug in something and (usually) get something else in return

sin : (-∞, +∞) → [-1, +1]

sin(1) = 0.84

sin(19.85) = 0.84

arcsin : [-1, +1] → [-π/2, +π/2]

arcsin(0.84) = 1

If `x∊[-π/2, +π/2]`, then you can apply the two functions consecutively and return to what you started with

sin: [-π/2,+π/2]→[-1,+1]

arcsin: [-1,+1]→[-π/2,+π/2]

(arcsin o sin): [-π/2,+π/2] → [-π/2,+π/2]

arcsin(sin(1)) = arcsin(0.84) = 1

arcsin: [-1,+1]→[-π/2,+π/2]

sin: [-π/2,+π/2]→[-1,+1]

(sin o arcsin): [-1,+1] → [-1,+1]

sin(arcsin(0.84)) = sin(1) = 0.84

However, if x does not lie in the range of arcsin, then you won't get the original value

sin: [11π/2,13π/2]→[-1,+1]

arcsin: [-1,+1]→[-π/2,+π/2]

(arcsin o sin): [11π/2,13π/2] → [-π/2,+π/2]

arcsin(sin(19.85)) = arcsin(0.84) = 1