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Rufina [12.5K]
3 years ago
5

I need help combining functions!

Mathematics
1 answer:
postnew [5]3 years ago
5 0
\bf \begin{cases}
f(x)=\cfrac{2}{x}\\\\
g(x)=\cfrac{x}{x+2}
\end{cases}\qquad g[\quad f(x)\quad ]=\cfrac{[f(x)]}{[f(x)]+2}

\bf (g\circ f)(x)\iff g[\quad f(x)\quad ]=\cfrac{\boxed{\frac{2}{x}}}{\boxed{\frac{2}{x}}+2}
\\\\\\
g[\quad f(x)\quad ]=\cfrac{\frac{2}{x}}{\frac{2x+2}{x}}\implies g[\quad f(x)\quad ]=\cfrac{2}{x}\cdot \cfrac{x}{2x+2}
\\\\\\
g[\quad f(x)\quad ]=\cfrac{2x}{2x^2+2x}\implies  g[\quad f(x)\quad ]=\cfrac{2x}{2x(x+1)}
\\\\\\
g[\quad f(x)\quad ]=\cfrac{1}{x+1}
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