Tag: functions and graphs

Let $f$ be an injective map with domain {x, y, z} and range {1, 2, 3} such that exactly one of the following statements is correct and the remaining are false :
$f (x) = 1, f (y) \sqrt 1, f (z) \sqrt 2$. The value of $f^{-1} (1)$ is

$c \to c\,\,is\,defined\,as\,f\left( x \right) = \frac{{ax + b}}{{cx + d}}\,\,bd \ne 0$.then f is a constant function when

$f:c \to c$ is defined as $f(x) = \dfrac{{ax + b}}{{cx + d}},bd \ne 0$ then $f$ is a constant function when,

If $f(n+1)=f(n)$ for all $n\in N, f(7)=5$  then  $f(35)=$

Let $f(x)$ is a cubic polynomial with real coefficients, $x\ \in R$ such that $f"(3)=0,\ f'(5)=0$  
If $f(3)=1$ and $f(5)=-3$, then $f(1)$ is equal to

The complete set of values of $x$ for which the function $f(x)=2\tan^{-1}x+\sin^{-1} \dfrac{2x}{1+x^{2}}$ behaves like a constant function with positive output is equal to

Let f be a polynomial function such that $f(3x)=f'(x).f"(x)$, for all $x\epsilon R$. Then :

If  $f \left( \dfrac { x + y } { 2 } \right) = \dfrac { f ( x ) + f ( y ) } { 2 }$  for all  $x , y \in R$  and  $f ^ { \prime } ( o ) = - 1 , f ( o ) = 1$  then  $f(2)=$

let $f(x)$ be a polynomial of degree $4$ having extreme values at $x=2$.if $\underset { x\rightarrow 0 }{ lim } \left( \frac { f\left( x \right)  }{ { x }^{ 2 } } +1 \right) =3$ then $f(1)$

If $\alpha$ and $\beta$ are the polynomial  $f(x)=x^2-5x+k$ such that $\alpha-\beta=1$, then value of k is