InverseFunction.md (511B)
1 # Inverse Function 2 3 L2 4 5 **Definition:** The inverse function of f(x) is defined as f^-1(x) where f^-1(x) maps from the codomain of f(x) to the domain of f(x). 6 7 As such, for a function to be invertible it must be a bijection. 8 9 ## Finding 10 11 The simplest way to find the inverse of a function is by swapping the y and x terms and then solving for y. 12 13 Consider: 14 15 $$ 16 f(x) = x^3 + 10 17 \newline 18 y = x^3 + 10 19 \newline 20 21 $$ 22 23 $$ 24 x = y^3 + 10 25 \newline 26 x+10 = y^3 27 \newline 28 y = \sqrt[3]{x+10} 29 $$ 30 31 $$ 32 f'(x) = \sqrt[3]{x+10} 33 $$ 34