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gavmur [86]
3 years ago
6

State whether f is a function

Mathematics
2 answers:
Alenkinab [10]3 years ago
5 0
<h2>Answer:</h2>

y=\pm (\frac{x}{6})^{\frac{1}{4}} \ is \ not \ a \ function

<h2>Step by step solution:</h2>

A function f from a set A to a set B is a relation that assigns to each element x in the set A exactly one element y in the set B. The set A is the domain (also called the set of inputs) of the function and the set B contains the range (also called the set of outputs). On the other hand, a function has an inverse function if and only if passes the Horizontal Line Test for Inverse Functions. This test tells us that a function f has an inverse function if and only if there is no any horizontal line that intersects the graph of f at more than one point. So the function is called one-to-one. The graph of f is shown below. As you can see, this function does not pass the Horizontal Line Test, therefore the inverse is not a function. However, let's find f^-{1}(x):

f(x)=6x^4 \\ \\ Substitute \ f(x) \ by \ y \\ \\ y=6x^4 \\ \\ Interchange \ x \ and \ y: \\ \\ x=6y^4 \\ \\ Solve \ for \ y: \\ \\ y^4=\frac{x}{6} \\ \\ Solving \\ \\y=\pm \sqrt[4]{\frac{x}{6}} \\ \\ \boxed{y=\pm \left(\frac{x}{6}\right)^{\frac{1}{4}}}

and this is not a function because there are elements in the set of inputs that match with two elements in the set of outputs.

Vika [28.1K]3 years ago
3 0

Answer:

(\frac{y}{6 })^{1/4}=f^{-1}(y)

Step-by-step explanation:

We have given a function.

f(x) = 6x⁴

We have to find the inverse of the given function.

Putting y=f(x) in given equation ,we have

y = 6x⁴

y/6 = x⁴

Taking 4th root to both sides of Above equation, we have

(\frac{y}{6})^{1/4}=x

Putting x = f⁻¹(y) in above equation, we have

(\frac{y}{6 })^{1/4}=f^{-1}(y)

Replacing y by x , we have

(\frac{±x}{6 })^{1/4}=f^{-1}(x) which is the answer.

f⁻¹(x) is not function because it assigns each value of x to two values of y.

Choice D is correct answer.

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