Minimum integral value of $\alpha$ for which graph of $f(x) = ||x -2| -\alpha|-5$ has exactly four $x-$intercepts-
$6$
$4$
$7$
$5$
If in greatest integer function, the domain is a set of real numbers, then range will be set of
A real valued function $f(x)$ satisfies the function equation $f(x - y) = f(x)f(y) - f(a - x)f(a + y)$ where a is a given constant and $f(0) = 1$, $f(2a - x)$ is equal to
The period of the function $f (x) =$$\frac{{|\sin x| + |\cos x|}}{{|\sin x - \cos x|}}$ is
Show that function $f : R \rightarrow\{ x \in R :-1< x <1\}$ defined by $f ( x )=\frac{x}{1+|x|^{\prime}} x \in R$ is one-one and onto function.
Let $f ( x )$ be a quadratic polynomial with leading coefficient $1$ such that $f(0)=p, p \neq 0$ and $f(1)=\frac{1}{3}$. If the equation $f(x)=0$ and $fofofof (x)=0$ have a common real root, then $f(-3)$ is equal to $........$