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

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

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

Let f : R $$\to$$ R be given by f(x) = | x2 $$-$$ 1 |, x$$\in$$R. Then,

f(x) is real valued function such that 2f(x) + 3f($$-$$x) = 15 $$-$$ 4x for all x$$\in$$R. Then f(2) =

Consider the functions f1(x) = x, f2(x) = 2 + loge x, x > 0. The graphs of the functions intersect

Given that f : S $$\to$$ R is said to have a fixed point at c of S if f(c) = c. Let f : [1, $$\infty$$) $$\to$$ R be defined by f(x) = 1 + $$\sqrt x ...

Let $$f(x) = 1 - \sqrt {({x^2})} $$, where the square root is to be taken positive, then

The domain of $$f(x) = \sqrt {\left( {{1 \over {\sqrt x }} - \sqrt {x + 1} } \right)} $$ is

Let $$f(x) = \sqrt {{x^2} - 3x + 2} $$ and $$g(x) = \sqrt x $$ be two given functions. If S be the domain of fog and T be the domain of gof, then

Let $$f:R \to R$$ be defined by $$f(x) = {x^2} - {{{x^2}} \over {1 + {x^2}}}$$ for all $$x \in R$$. Then,

Consider the function f(x) = cos x2. Then,

Let a > b > 0 and I(n) = a1/n $$-$$ b1/n, J(n) = (a $$-$$ b)1/n for all n $$ \ge $$ 2, then

The domain of definition of $$f(x) = \sqrt {{{1 - |x|} \over {2 - |x|}}} $$ is

If f : R $$ \to $$ R be defined by f (x) = ex and g : R $$ \to $$ R be defined by g(x) = x2. The mapping gof : R $$ \to $$ R be defined by (gof) (x) =...

For 0 $$ \le $$ p $$ \le $$ 1 and for any positive a, b; let I(p) = (a + b)p, J(p) = ap + bp, then

If the polynomial $$f(x) = \left| {\matrix{ {{{(1 + x)}^a}} & {{{(2 + x)}^b}} & 1 \cr 1 & {{{(1 + x)}^a}} & {{{(2 + x)}^b}} \...

Let $$f:R \to R$$ be such that f is injective and $$f(x)f(y) = f(x + y)$$ for $$\forall x,y \in R$$. If f(x), f(y), f(z) are in G.P., then x, y, z are...

Let $$f(x) = {x^{13}} + {x^{11}} + {x^9} + {x^7} + {x^5} + {x^3} + x + 19$$. Then, f(x) = 0 has

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

Let f and g be periodic functions with the periods T1 and T2 respectively. Then f + g is

Consider the function $$y = {\log _a}(x + \sqrt {{x^2} + 1} ),a > 0,a \ne 1$$. The inverse of the function