The graph below depicts a function f(x)\displaystyle {f{{\left({x}\right)}}}. Its two asymptotes are indicated in red:

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The graph below depicts a function g(x)\displaystyle {g{{\left({x}\right)}}}. Its one asymptote is indicated in red:

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lim⁡x→1+  f(g(x))=\displaystyle \lim_{{{x}\to{1}^{+}}}\ \ {f{{\left({g{{\left({x}\right)}}}\right)}}}=

lim⁡x→2−  f(g(x))=\displaystyle \lim_{{{x}\to{2}^{{-}}}}\ \ {f{{\left({g{{\left({x}\right)}}}\right)}}}=

lim⁡x→2+  f(g(x))=\displaystyle \lim_{{{x}\to{2}^{+}}}\ \ {f{{\left({g{{\left({x}\right)}}}\right)}}}=

lim⁡x→∞  f(g(x))=\displaystyle \lim_{{{x}\to\infty}}\ \ {f{{\left({g{{\left({x}\right)}}}\right)}}}=

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