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

1 Answer
marfre
Feb 24, 2017

#f^-1 = (x^5-4)/5#

Explanation:

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

Swap #y# for #x# and #x# for #y#: #x = root(5)(5y+4)#

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

Solve for #y#.

  1. 5th power both sides: #x^5 = ((5y+4)^(1/5))^5 = 5y+4#
  2. Isolate #y#: #5y = x^5-4#
  3. Simplify: #y = (x^5-4)/5#

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

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