WB JEE 2008 | Functions Question 2 | Mathematics

WB JEE 2008

MCQ (Single Correct Answer)

-0.25

The function $$f(x) = \log \left( {{{1 + x} \over {1 - x}}} \right)$$ satisfies the equation

$$f(x + 2) - 2f(x + 1) + f(x) = 0$$

$$f(x) + f(x + 1) = f(x(x + 1))$$

$$f(x) + f(y) = f\left( {{{x + y} \over {1 + xy}}} \right)$$

$$f(x + y) = f(x)f(y)$$

WB JEE 2008

MCQ (Single Correct Answer)

-0.25

The equation e^x + x $$-$$ 1 = 0 has, apart from x = 0

One other real root

Two real roots

No other real root

Infinite number of real roots

WB JEE 2009

MCQ (Single Correct Answer)

-0.25

A mapping from IN to IN is defined as follows:

$$f:IN \to IN$$

$$f(n) = {(n + 5)^2},\,n \in IN$$

(IN is the set of natural numbers). Then

f is not one-to-one

f is onto

f is both one-to-one and onto

f is one-to-one but not onto

WB JEE 2009

MCQ (Single Correct Answer)

-0.25

The domain of definition of the function $$f(x) = \sqrt {1 + {{\log }_e}(1 - x)} $$ is

$$ - \infty < x \le 0$$

$$ - \infty < x \le {{e - 1} \over e}$$

$$ - \infty < x \le 1$$

$$x \ge 1 - e$$

WB JEE Subjects