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 $f(x)=f \frac{x+1}{x+2}$ are
(1996, 1M)
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Answer:
Correct Answer: 11. (a)
Solution:
- Given,
$$ f(x)=2 x+\sin x $$
$\Rightarrow$
$$ f^{\prime}(x)=2+\cos x \quad \Rightarrow \quad f^{\prime}(x)>0, \forall x \in R $$
which shows $f(x)$ is one-one, as $f(x)$ is strictly increasing. Since, $f(x)$ is increasing for every $x \in R$,
$\therefore f(x)$ takes all intermediate values between $(-\infty, \infty)$.
Range of $f(x) \in R$.
Hence, $f(x)$ is one-to-one and onto.
