The range of the function $$f(x) = {\log _e}\sqrt {4 - {x^2}} $$ is given by

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

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

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

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

The domain of the function $$f(x) = \sqrt {{{\cos }^{ - 1}}\left( {{{1 - |x|} \over 2}} \right)} $$ is

For what values of x, the function $$f(x) = {x^4} - 4{x^3} + 4{x^2} + 40$$ is monotone decreasing?

The minimum value of $$f(x) = {e^{({x^4} - {x^3} + {x^2})}}$$ is

The period of the function f(x) = cos 4x + tan 3x is

The even function of the following is

If f(x + 2y, x $$-$$ 2y) = xy, then f(x, y) is equal to

If $g(f(x))=|\sin x|$ and $f(g(x))=(\sin \sqrt{x})^2$, then

If $f(x)=\frac{3 x-4}{2 x-3}$, then $f(f(f(x)))$ will be

Let $u+v+w=3, u, v, w \in \mathbb{R}$ and $f(x)=u x^2+v x+w$ be such that $f(x+y)=f(x)+f(y)+x y$, $\forall x, y \in \mathbb{R}$. Then $f(1)$ is equal to

If $f(x)$ and $g(x)$ are two polynomials such that $\phi(x)=f\left(x^3\right)+x g\left(x^3\right)$ is divisible by $x^2+x+1$, then

Let $$\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}$$ be a function defined by $$\mathrm{f}(x)=\frac{\mathrm{e}^{|x|}-\mathrm{e}^{-x}}{\mathrm{e}^x+\mathrm{e}^{-x}}$$, then

For every real number $$x \neq-1$$, let $$\mathrm{f}(x)=\frac{x}{x+1}$$. Write $$\mathrm{f}_1(x)=\mathrm{f}(x)$$ & for $$\mathrm{n} \geq 2, \mathrm{f}_{\mathrm{n}}(x)=\mathrm{f}\left(\mathrm{f}_{\mathrm{n}-1}(x)\right)$$. Then $$\mathrm{f}_1(-2) \cdot \mathrm{f}_2(-2) \ldots . . \mathrm{f}_{\mathrm{n}}(-2)$$ must be

The equation $$2^x+5^x=3^x+4^x$$ has

In the interval $$( - 2\pi ,0)$$, the function $$f(x) = \sin \left( {{1 \over {{x^3}}}} \right)$$.

Domain of $$y = \sqrt {{{\log }_{10}}{{3x - {x^2}} \over 2}} $$ is

Let $$f(x) = {(x - 2)^{17}}{(x + 5)^{24}}$$. Then

Let $$f(n) = {2^{n + 1}}$$, $$g(n) = 1 + (n + 1){2^n}$$ for all $$n \in N$$. Then

The maximum value of $$f(x) = {e^{\sin x}} + {e^{\cos x}};x \in R$$ is

$$f:X \to R,X = \{ x|0 < x < 1\} $$ is defined as $$f(x) = {{2x - 1} \over {1 - |2x - 1|}}$$. Then

Show that sin x is a monotonic increasing function of x in 0 < x < $$\pi$$/2.

The function $$\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}$$ defined by $$\mathrm{f}(x)=\mathrm{e}^x+\mathrm{e}^{-x}$$ is :

Choose the correct statement :

Let $$f(x) = {x^2} + x\sin x - \cos x$$. Then

Let p(x) be a polynomial with real co-efficient, p(0) = 1 and p'(x) > 0 for all x $$\in$$ R. Then