Mathematics: F(x)=1/x-2 , g(x)=2x+1/xa. use composition to prove whether or not the functions are inverses of each other.b. express the domain of the compositions using interval notation.

F(x)=1/x-2 , g(x)=2x+1/xa. use composition to - id12211752339, elijahchloesunshine

Ответ:

quetzaliescalona

30.12.2021

Mathematics

A. They are inverses of each other.

Step-by-step explanation:

If they are inverses of each other then f(g(x)) will be = x.

f(g(x)) = 1 / ( (2x + 1)/ x) - 2)

= 1 / ( 2x + 1 - 2x)/ x

= 1 / 1/x

= x.

So they ARE inverses of each other.

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Ответ:

laylac45531

30.12.2021

Mathematics

Yes, they are inverse of each other.

Domain = $(-\infty, \infty)$

Step-by-step explanation:

We re given the following:

$f(x) = \frac{1}{x-2}\\g(x) = \frac{2x+1}{x}$

If we calculate the composite function, it will be of the form:

$f(g(x)) = \frac{1}{\frac{2x+1}{x}-2} \\= \frac{x}{2x + 1 - 2x}\\= x$

$g(f(x)) = \frac{2(\frac{1}{x-2}) + 1}{x-2}\\= \frac{2+x-2}{1}\\\\= x$

Since, f(g(x)) = g(f((x)) = x, the functions are inverse of each other.

The domain of composite functions, f(g(x)) and g(f((x)) are the values that x can take, so the domain for composite number is all real numbers that is $(-\infty, \infty)$

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Ответ:

walkerobrien5

03.01.2020

Mathematics

Cubes to the reid power

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F(x)=1/x-2 , g(x)=2x+1/x
a. use composition to prove whether or not the functions are inverses of each other.
b. express the domain of the compositions using interval notation.

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