Does the function: f(x)=x 4 +6x have an inversefunction? I really dont understan

Question

Does the function: f(x)=x4+6x have an inversefunction? I really dont understand how to find an inverse for thisfunction. I mean i get the Horixontal Line Test and all of that butI dont understand how to algebraically show the inversefunction. Could you please help me out? Thank you. Does the function: f(x)=x4+6x have an inversefunction? I really dont understand how to find an inverse for thisfunction. I mean i get the Horixontal Line Test and all of that butI dont understand how to algebraically show the inversefunction. Could you please help me out? Thank you.

Explanation / Answer

the previous post has the right general idea but you cannotchange addition to multiplication as done ver early in the problem... since it is a 4th degree polynomial with a positive leadingcoefficient, the graph has "Up-Up" end behvaior using the LeadingCoefficient Test ... this means that the graph must fail theHorizontal Line Test and does not have an inverse that is afunction .... thus the process of interchanging x and y andre-solving for y to get it into function form not applicable tothis problem

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