If $f(x)=2\{x\}+5x$,where $\{x\}$ is the fractional part function,then $f(-1.4)$ is

Let $S=(0,1) \cup(1,2) \cup(3,4)$ and $T=\{0,1,2,3\}$. Then which of the following statements is(are) true?
$(A)$ There are infinitely many functions from $S$ to $T$.
$(B)$ There are infinitely many strictly increasing functions from $S$ to $T$.
$(C)$ The number of continuous functions from $S$ to $T$ is at most $120$.
$(D)$ Every continuous function from $S$ to $T$ is differentiable.

Let $f(x) = \frac{x^2 - 4}{x^2 + 4}$ for $|x| > 2$. Then the function $f: (- \infty, -2] \cup [2, \infty) \to (-1, 1)$ is

Let $f : R \to R$ be a function defined by $f(x) = - \frac{|x|^3 + |x|}{1 + x^2}$; then the graph of $f(x)$ lies in the :-

Let $f(x) = a^x$ $(a > 0)$ be written as $f(x) = f_1(x) + f_2(x)$,where $f_1(x)$ is an even function and $f_2(x)$ is an odd function. Then $f_1(x + y) + f_1(x - y)$ equals

If $X$ and $Y$ are two non-empty sets where $f: X \to Y$ is a function defined such that $f(C) = \{f(x) : x \in C\}$ for $C \subseteq X$ and $f^{-1}(D) = \{x : f(x) \in D\}$ for $D \subseteq Y$,then for any $A \subseteq X$ and $B \subseteq Y$,which of the following is true?