GATE CSE 2015 | Set 1 | Question: 5

Question

If $g(x) = 1 - x$ and $h(x) = \frac{x}{x-1}$, then $\frac{g(h(x))}{h(g(x))}$ is:

• A. $\frac{h(x)}{g(x)}$
• B. $\frac{-1}{x}$
• C. $\frac{g(x)}{h(x)}$
• D. $\frac{x}{(1-x)^{2}}$

Comments

Please edit the question! Correct question is given below:

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Thanks. Edited :)

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For fast calculation we can consider x = 2 and then try to solve 

Answer 1

option a) is correct.

$g\left(h\left(x\right)\right) =g\left(\frac{x}{x-1}\right)$
    $=1-\frac{x}{x-1}$
    $= \frac{-1}{x-1}$

$h\left(g\left(x\right)\right) =h(1-x)$
  $=\frac{1-x}{-x}$

$\frac{g(h(x))}{h(g(x))} = \frac{x}{(1-x)(x-1)} = \frac{h(x)}{g(x)}$
       

option A)

Comments

sir how iitk declare ans as a?

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Answer is A only. I guess the answer was put for a different question- corrected now :)

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But why is the answer not D then?

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 @kirtipurohit hope you get this now

 

Answer 2

.

Answer 3

Correct answer is A because of

(x/x-1)*(1/1-x)

g(x) = 1-x and h(x)=x/x-1

so h(x)/g(x)

Answer 4

The correct answer is (A) h(x) / g(x)

Answer 5

substitute x =2 and match it with the given option u will get easily we cant substitute 0or 1 as it will lead to undefined solution.