Find the inverse of the following function. (i) `f(x) = sin^(-1)(x/3), x in [-3,3]` (ii) `f(x) = 5^(log_e x), x gt 0` (iii) `f(x) = log_e (x+sqrt(x^2+1))`

Answer

(i) `f^(-1)(x)=3sinx` (ii) `f^(-1)(x)=(-3+sqrt(5+4e^(x)))/2`
(iii) `f^(-1)(x)=x^(log_(5^(e))),x gt 0` (iv) `f^(-1)(x)=1/2(e^(x)-e^(-x))`
(v) `f^(-1)(x)={{:(x",", x lt 1),(sqrt(x)",", 1 le x le 16),(x^(2)/64",", x gt 16):}`