If g(x)=(1)/(f(x)) and f(x)=x, x ≠ 0 , then which one of the following is correct

Correct answer: B. f(f(g(3( g(f(x)))))))=g(g(f(g(f(x)))))) aligned & f(x)=x & g(x)=1 / x aligned Putting these values in the options, only (2) is correct.

NDA 2015

Exam: NDA
Year: 2015
Subject: Mathematics
Chapter: Functions

NDA 2015 · Mathematics · Functions

If g(x)=(1)/(f(x)) and f(x)=x, x ≠ 0 , then which one of the...

g(x)=\frac{1}{f(x)}

and

f(x)=x, x \neq 0

, then which one of the following is correct

Options

A $\quad \mathrm{f}(\mathrm{f}(\mathrm{f}(\mathrm{g}(\mathrm{g}(\mathrm{f}(\mathrm{x})))))))=\mathrm{g}(\mathrm{g}(\mathrm{f}(\mathrm{g}(\mathrm{f}(\mathrm{x}))))))$
B $\quad \mathrm{f}(\mathrm{f}(\mathrm{g}(3(\mathrm{ g}(\mathrm{f}(\mathrm{x})))))))=\mathrm{g}(\mathrm{g}(\mathrm{f}(\mathrm{g}(\mathrm{f}(\mathrm{x}))))))$
C $\quad \mathrm{f}(\mathrm{g}(\mathrm{f}(\mathrm{g}(\mathrm{g}(\mathrm{f}(\mathrm{g}(\mathrm{x}))))))=\mathrm{g}(\mathrm{g}(\mathrm{f}(\mathrm{g}(\mathrm{f}(\mathrm{x}))))))$
D $\quad \mathrm{f}(\mathrm{f}(\mathrm{f}(\mathrm{f}(\mathrm{f}(\mathrm{f}(\mathrm{x}))))))=\mathrm{f}(\mathrm{f}(\mathrm{f}(\mathrm{g}(\mathrm{f}(\mathrm{x})))))$

Correct answer

B. $\quad \mathrm{f}(\mathrm{f}(\mathrm{g}(3(\mathrm{ g}(\mathrm{f}(\mathrm{x})))))))=\mathrm{g}(\mathrm{g}(\mathrm{f}(\mathrm{g}(\mathrm{f}(\mathrm{x}))))))$

Step-by-step solution

\begin{aligned} & f(x)=x \\ & g(x)=1 / x \end{aligned}

Putting these values in the options, only (2) is correct.

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