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Dahasolnce [82]
3 years ago
9

Determine if the two functions f and g are inverses of each other algebraically. If not, why not?

Mathematics
1 answer:
yKpoI14uk [10]3 years ago
6 0

The given functions are

f(x) = \frac{3}{x-5} , g(x) = \frac{3+5x}{x}

First we find fog(x)= f(g(x))

So we need to substitute the value of g(x) for x in f(x), that is

f(g(x)) = \frac{3}{\frac{3+5x}{x}-5} = \frac{3x}{3+5x-5x}

= \frac{3x}{3} = x

Now we need to check the value of gof(x)

gof(x) = g(f(x))

So we need to substitute the value of f(x) in g(x), that is

g(f(x))=\frac{3+5*\frac{3}{x-5}}{\frac{3}{x-5}}= \frac{3x-15+15}{3}

=\frac{3x}{3} = x

And since

fog(x) =gof(x) =x

So the functions are inverse of each other .

Correct option is C .

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I got this equation by using vertical angles to create a complimentary angle pair (they sum to 90 degrees).

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\bf {{ a}}\%\ of\ b \implies  \cfrac{{{ a}}}{100}\cdot b\implies {{ a}}\div 100\cdot b\\\\
-----------------------------\\\\
thus
\\\\

\begin{cases}
{{ 1}}\%\ of\ 400 \implies  \cfrac{{{ 1}}}{100}\cdot 400\implies {{1}}\div 100\cdot 400\\
--------------\\
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