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• #5959

Dear Sir,

Could you please support for clearing my doubts:

1. Math: How to find a domain & range of fog,(x) , gof(x) can you help me.
2. stat: How to identify when to use addition and multiplication rule, Npr, ncr. Means tricky questions the process of simplifications.

Regards
Ayyakutti A

• #5960

$\begin{gathered} {\text{Let us understand this with an example:}} \hfill \\ f(x) = \frac{1}{{1 + x}} \hfill \\ g(x) = \ln x \hfill \\ fog(x) = f[g(x)] = f[\ln x] = \frac{1}{{1 + (\ln x)}} \hfill \\ ({\text{Put }}g(x){\text{ in place of }}x{\text{ in }}f(x){\text{, you will get }}fog(x)) \hfill \\ {\text{To find domain, you need to calculate the set of all values for which the function }} \hfill \\ {\text{is defined}}{\text{.}} \hfill \\ {\text{But in exam, just try to find out the value of x at which the function is not defined}}{\text{.}} \hfill \\ fog(x) = \frac{1}{{1 + (\ln x)}} \hfill \\ {\text{Here, }}fog(x){\text{ is not defined when denominator }} = 0{\text{, and when }}\ln x{\text{ is not defined}} \hfill \\ \ln x{\text{ is not defined for negative value of x, hence }}x{\text{ }} > 0 \hfill \\ {\text{denominator of }}fog(x){\text{ can not be zero, hence x}} \ne \frac{1}{e} \hfill \\ {\text{hence domain = all positive value except }}\frac{1}{e} \hfill \\ {\text{Similarly you can calculate the range, it is set of all possible value of outcome for }} \hfill \\ {\text{the domain as input to function}}{\text{.}} \hfill \\ \hfill \\ {\text{Tip for Exam: Use online calculator to eliminate wrong options}}{\text{.}} \hfill \\ \end{gathered}$