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anonymous
 one year ago
given f(x)=3x^6 find f^1(x). then state whether f^1(x) is a function
anonymous
 one year ago
given f(x)=3x^6 find f^1(x). then state whether f^1(x) is a function

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, 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
 one year ago
Best ResponseYou've already chosen the best response.1Rule: 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

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so it's like saying x^2 = 4 has the two solutions x = 2 or x = 2 shorthand: \(\Large x = \pm 2\)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you're welcome
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