Functions 2 Question 15

16. If y=f(x)=x+2x1, then

(1984, 3M)

(a) x=f(y)

(b) f(1)=3

(c) y increases with x for x<1

(d) f is a rational function of x

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Answer:

Correct Answer: 16. (b, c)

Solution:

  1. Given, y=f(x)=x+2x1

yxy=x+2x(y1)=y+2x=y+2y1x=f(y)

Here, f(1) does not exist, so domain R1

dydx=(x1)1(x+2)1(x1)2=3(x1)2

f(x) is decreasing for all xR1.

Also, f is rational function of x.

Hence, (a) and (d) are correct options.



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