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What is the inverse function of #f(x)=3x^4#?

Answer 1

Liam Brennan

With its natural domain of #(-oo, oo)#, that function is not one-to-one. It does not have an inverse.

If we restrict the domain to some subset of #[0,oo)#, then the function has an inverse:

#y = 3x^4#

#x^4 = y/3#,

#x = root(4)(y/3)#

So the inverse function is #g(x) = root(4)(x/3)# (Rationalize the denominator if you wish to get #g(x) = root(4)(27x)/3#.)

On the other hand: It we restrict the domain to a subset of #(-oo, 0]#, then the inverse is #h(x) = -root(4)(x/3)#

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Answer 2

James Allen

The inverse function of f(x) = 3x^4 is f^(-1)(x) = (x/3)^(1/4).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.