How do you find the inverse function #f(x) = -3 x^7-2#?

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Answer 1 · 2015-07-18T09:16:53

Let #y=f(x)# and apply a sequence of operations to both sides of the equation to isolate #x# and find:

#f^(-1)(y) = -root(7)((y+2)/3)#

Let #y = f(x) = -3x^7-2#

Add #2# to both ends to get:

#y+2 = -3x^7#

Divide both sides by #-3# to get:

#x^7 = -(y+2)/3#

Take #7#th root to get:

#x = root(7)(-(y+2)/3) = -root(7)((y+2)/3)# (since #(-1)^7 = -1#)

So #f^(-1)(y) = -root(7)((y+2)/3)#