anonymous
  • anonymous
given f(x)=3x^6 find f^-1(x). then state whether f^-1(x) is a function
Mathematics
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chestercat
  • chestercat
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anonymous
  • anonymous
Yes, the given function is f^-1(x) or the inverse function of x. This is because since the inverse function of x is equal to the given equation or in other words, f(x)=3x^6 is 3x^6=x. If we simplify this equation, we get x^5=1/3 in which x is the fifth power of 1/3. Since the fifth power of 1/3 has only one answer which is positive, the given equation is a function.
jim_thompson5910
  • jim_thompson5910
Rule: if the degree of the polynomial is even, then it won't have an inverse because it fails the horizontal line test in this case, let's say x = 2 x^6 = 2^6 = 64 now let's say x = -2 x^6 = (-2)^6 = 64 both inputs lead to the same output. So this is one example of how x^6 fails the horizontal line test
anonymous
  • anonymous
so y=+(x/3)^6?

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jim_thompson5910
  • jim_thompson5910
so it's like saying x^2 = 4 has the two solutions x = 2 or x = -2 shorthand: \(\Large x = \pm 2\)
anonymous
  • anonymous
Thank you
jim_thompson5910
  • jim_thompson5910
you're welcome

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