How do you find the inverse of #f(x)=3x^4#?

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Answer 1 · 2018-04-05T12:57:10

#f^-1(x) = + root(4)(x/3)#

#f(x)=3x^4 ; x>=0#
#y=3x^4#
#x=3y^4#
#y^4=x/3#
#y= root(4)(x/3)#
#f^-1(x) = + root(4)(x/3)#

Note: in the case of #f(x) = 3x^4# there are two values of #x# that

give the same #f(x)#. This is because both# f(x) = x^4# and also

#f(−x) = x^4#. We cannot define #f^-1# of something to be two

different things. So we restrict the domain of the function for

#x>=0#

graph{3x^4 [-10, 10, -5, 5]} [Ans]