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multiple choice correct type: if y = f(x)=x+2/x-1 then options:a-f(1)=3 b-y is increasing with x for x less than 1 c-f(y)=x d-f is a rational function of x. not able to click option c and d please explain how to reason them. answer:only c

multiple choice correct type: if y = f(x)=x+2/x-1 then options:a-f(1)=3  b-y is increasing with x for x less than 1 c-f(y)=x d-f is a rational function of x.  not able to click option c and d please explain how to reason them. answer:only c

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1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below
y = f(x) = \frac{x+2}{x-1}
f(y) = \frac{y+2}{y-1}
f(y) = \frac{\frac{x+2}{x-1}+2}{\frac{x+2}{x-1}-1}
f(y) = \frac{\frac{x+2+2x-2}{x-1}}{\frac{x+2-x+1}{x-1}}
f(y) = \frac{3x}{3} = x
f(x) ia an rational function of x.

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