Question

given f(x)=3x^6 find f^-1(x). then state whether f^-1(x) is a function

Answer 1

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.

Answer 2

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

Answer 3

so y=+(x/3)^6?

Answer 4

so it's like saying x^2 = 4 has the two solutions x = 2 or x = -2

shorthand: \(\Large x = \pm 2\)

Answer 5

Thank you

Answer 6

you're welcome