How do you find the inverse of f(x)=root5(5x+4)f(x)=55x+4?

1 Answer
Feb 24, 2017

f^-1 = (x^5-4)/5f1=x545

Explanation:

Let y = f(x): y = root(5)(5x+4)y=f(x):y=55x+4

Swap yy for xx and xx for yy: x = root(5)(5y+4)x=55y+4

Remember that root(5)( ) = ( )^(1/5) 5=()15 so x = (5y+4)^(1/5)x=(5y+4)15

Solve for yy.

  1. 5th power both sides: x^5 = ((5y+4)^(1/5))^5 = 5y+4x5=((5y+4)15)5=5y+4
  2. Isolate yy: 5y = x^5-45y=x54
  3. Simplify: y = (x^5-4)/5y=x545

The inverse function f^-1 = (x^5-4)/5f1=x545