Range of $f(x) = \;[x]\; - x$ is
$[0, 1]$
$(-1, 0]$
$R$
$(-1, 1)$
Let $A=\{0,1,2,3,4,5,6,7\} .$ Then the number of bijective functions $f: A \rightarrow A$such that $f(1)+f(2)=3-f(3)$ is equal to $.....$
Show that none of the operations given above has identity.
The range of the function $f(x) = \frac{{\sqrt {1 - {x^2}} }}{{1 + \left| x \right|}}$ is
Let a function $f : R \rightarrow R$ is defined such that $3f(2x^2 -3x + 5) + 2f(3x^2 -2x + 4) = x^2 -7x + 9\ \ \ \forall x \in R$, then the value of $f(5)$ is-