Tag: introduction to sets

If $ P ( X ) = x ^ { 3 } - 3 x ^ { 2 } + 2 x + 5 $ and P ( a ) = P ( b ) = P ( c ) = 0 then the value of ( 2 - a ) ( 2 - b ) ( 2 - c ) is

If f : R $\rightarrow$ R, g : R $\rightarrow$ R and h : R $\rightarrow$ R is such that $f(x) = x^2, g(x) = tan  x$ and $h(x) = log  x$, then the value of [ho(gof)], if $x = \displaystyle \dfrac{\pi}{2}$ will be

If f is a constant function and f(100)=100  then f(2007)=_____

The number of elements of an identity function defined on a set containing four elements is______

On differentiating an identity function, we get?

If $f,g,h$ are three functions from a set of positive real numbers into itself satisfying the condition,
$f(x) \cdot g(x)=h \sqrt{x^2 + y^2}$ such that $x,y \epsilon (0,\infty)$.then, $\dfrac{f(x)}{g(x)}$ is a?

A constant function is a periodic function.

Let $f(-2, 2)\rightarrow(-2, 2)$ be a continuous function given $f(x)=f{(x}^{2})$. Given $f(0)=\dfrac{1}{2}$ then the $4f(\dfrac{1}{2})$

If $f\left( x \right)$ is a function satisfying  $f\left( x \right).f\left( {\frac{1}{x}} \right) = f\left( x \right) + f\left( {\frac{1}{x}} \right)$ and $f\left( 4 \right) = 65$ then find $f\left( 6 \right)$

Let $f\left( x \right) = p{x^2} + qx - \left( {{a^2} + {b^2} + {c^2} - ab - bc - ca} \right),\,\left( {p,q,a,b,c \in R} \right)(a,b,c$ are distinct). If both roots of $f(x)=0$ are non-real, then