A) \[{{f}_{3}}(x)\]
B) \[{{f}_{1}}(x)\]
C) \[{{f}_{2}}(x)\]
D) \[\frac{1}{x}{{f}_{3}}(x)\]
Correct Answer: A
Solution :
\[{{f}_{1}}(x)=\frac{1}{x},\] \[{{f}_{2}}(x)=1-x\], \[{{f}_{3}}(x)=\frac{1}{1-x}\] |
\[({{f}_{2}}ojo{{f}_{1}})(x)={{f}_{3}}(x)\] |
\[({{f}_{2}}oj)\left( \frac{1}{x} \right)=\frac{1}{1-x}\] |
\[{{f}_{2}}\left( J\left( \frac{1}{x} \right) \right)=\frac{1}{1-x}\] |
\[1-J\left( \frac{1}{x} \right)=\frac{1}{1-x}\] |
\[1-\frac{1}{1-x}=J\left( \frac{1}{x} \right)\] |
\[\Rightarrow \] \[J\left( \frac{1}{x} \right)=\frac{1}{1-\frac{1}{x}}={{f}_{3}}(x).\] |
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