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Kisachek [45]
2 years ago
14

Evaluate 2/3 (10-6) 1/2 ​

Mathematics
1 answer:
Studentka2010 [4]2 years ago
4 0

Answer:

=  \frac{2}{3} (10 - 6) \frac{1}{2}

=  \frac{2}{3} (4) \frac{1}{2}

=  \frac{8}{3}  \times  \frac{1}{2}

=  \frac{4}{3}

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<h2>Answer:</h2>

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<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}}}

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<h2>D) - 9/7</h2>

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3 years ago
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