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If f(x)=1/x and g(x)=x/x^2+1
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06 Feb 2024, 01:42
06 Feb 2024, 01:42
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Question Stats:
71% (01:23) correct
28% (02:20) wrong based on 7 sessions
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If \(f(x)=\frac{1}{x}\) and \(g(x)=\frac{x}{x^2+1}\) for all \(x>0\) which opf the following statements are correct?
Indicate all that apply
A. \(f(g(2))=\frac{5}{2}\)
B. \(g(f(x))=x\)
C. \(g(f(x))=g(x)\)
Indicate all that apply
A. \(f(g(2))=\frac{5}{2}\)
B. \(g(f(x))=x\)
C. \(g(f(x))=g(x)\)
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GRE Geometry Formulas
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If f(x)=1/x and g(x)=x/x^2+1
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09 Feb 2024, 13:30
09 Feb 2024, 13:30
1
\(f(g(2)) = f(\frac{2}{2^2+1}) = \frac{5}{2}\)
\(g(f(x)) = f(\frac{1}{x}) = \frac{\frac{1}{x}}{(\frac{1}{x})^2+1}
= \frac{x^2}{x^2} * \frac{\frac{1}{x}}{(\frac{1}{x})^2+1} = \frac{x}{x^2+1} = g(x)\)
\(g(f(x)) = f(\frac{1}{x}) = \frac{\frac{1}{x}}{(\frac{1}{x})^2+1}
= \frac{x^2}{x^2} * \frac{\frac{1}{x}}{(\frac{1}{x})^2+1} = \frac{x}{x^2+1} = g(x)\)
gmatclubot
If f(x)=1/x and g(x)=x/x^2+1 [#permalink]
09 Feb 2024, 13:30
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