Functions 3 Question 11

11. If f is an even function defined on the interval (5,5), then four real values of x satisfying the equation f(x)=fx+1x+2 are

(1996, 1M)

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Answer:

Correct Answer: 11. (a)

Solution:

  1. Given,

f(x)=2x+sinx

f(x)=2+cosxf(x)>0,xR

which shows f(x) is one-one, as f(x) is strictly increasing. Since, f(x) is increasing for every xR,

f(x) takes all intermediate values between (,).

Range of f(x)R.

Hence, f(x) is one-to-one and onto.



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