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

f(x)=3/x-5 ; g(x)= 3+5x/x

A. No, ( f o g ) (x)= 3/5x-3
B. No, (f o g ) (x) =- 3/5x-3
C. Yes

Respuesta :

caylus

Hello,

Answer C

[tex] f(x)=y=\dfrac{3}{x-5}\\

Exchanging\ x\ and\ y\\

x=\dfrac{3}{y-5}\\

\Rightarrow\ y-5=\dfrac{3}{x}\\

\Rightarrow\ y=\dfrac{3}{x}+5\\

\Rightarrow\ y=\dfrac{3}{x}+\dfrac{5x}{x}\\

\Rightarrow\ y=\dfrac{3+5x}{x}=g(x)\\
[/tex]

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