A) fog is an increasing function
B) fog is a decreasing function
C) fog is neither increasing nor decreasing
D) None of the above
Correct Answer: A
Solution :
Let\[{{x}_{1}},{{x}_{2}}\in R\]such that\[{{x}_{1}}<{{x}_{2}}\]. Then, \[{{x}_{1}}<{{x}_{2}}\] \[\Rightarrow \] \[f({{x}_{1}})<f({{x}_{2}})\] (\[\because \]\[f\]is an increasing function) \[\Rightarrow \] \[g\{f({{x}_{1}})\}<g\{f({{x}_{2}})\}\] (\[\because \]is an increasing function) \[\Rightarrow \] \[gof({{x}_{1}})<gof({{x}_{2}})\] Hence,\[gof\]is an increasing function.
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