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zysi [14]
3 years ago
7

Given f(x)=8x^5, find f^-1(x) Then state whether f^1(x) is a function.

Mathematics
1 answer:
irina1246 [14]3 years ago
6 0

Answer:

f^-1(x) = (x/8)^(1/5) is a function

Step-by-step explanation:

The inverse of a function is the function reflected across the line y=x. This results in the coordinate points (x,y) of the function becoming (y,x) for the inverse function. Algebraically to find the inverse, switch the x and y locations and solve for y.

y = 8x^5

x = 8y^5

x/8 = y^5

(5)√(x/8) = y

This is a fifth root of (x/7) also written in exponents as y = (x/8)^(1/5).

This is a function. While it appears not to be a function because the middle portion over the origin appears vertical, it is a function because the middle portion over the origin is changing and graphing software shows it has no input with more than one output. Without graphing software you would rule it is not a function.

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A product of two (or more) factor can be zero if and only if at least one of the factors is zero.

In other words, you cannot multiply two non-zero real numbers, and have zero as a result.

So, if we want the product of these two factors to be zero, at least one of them has to be zero.

The first factor is zero if

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