For $0 \leq x \leq 1$,what type of function is $f(x) = |x| + |x - 1|$?

Let $A = \{x_1, x_2, x_3, \dots, x_7\}$ and $B = \{y_1, y_2, y_3\}$ be two sets containing seven and three distinct elements respectively. Then the total number of functions $f: A \to B$ which are onto,if there exist exactly three elements $x$ in $A$ such that $f(x) = y_2$,is equal to

For real $x,$ let $f(x) = x^3 + 5x + 1,$ then

Show that the function $f: N \rightarrow N$ given by $f(x) = 2x$ is one-one but not onto.

If $f : R \rightarrow R$ is defined as $f(x) = x - [x] + 3$,$\forall x \in R$,then $f$ is

Let $A = \{1, 2, 3, \ldots, n\}$ and $B = \{a, b\}$. If the number of onto functions from $A$ to $B$ is $62$,then the number of subsets of $A$ containing exactly three elements is: