Let $A=\{1,2,3,4,5\}$ and $B=\{1,2,3,4,5,6\}$. Then the number of functions $f: A \rightarrow B$ satisfying $f(1)+f(2)=f(4)-1$ is equal to
$360$
$361$
$362$
$363$
The value of $b$ and $c$ for which the identity $f(x + 1) - f(x) = 8x + 3$ is satisfied, where $f(x) = b{x^2} + cx + d$, are
Let $P(x)$ be a polynomial with real coefficients such that $P\left(\sin ^2 x\right)=P\left(\cos ^2 x\right)$ for all $x \in[0, \pi / 2)$. Consider the following statements:
$I.$ $P(x)$ is an even function.
$II.$ $P(x)$ can be expressed as a polynomial in $(2 x-1)^2$
$III.$ $P(x)$ is a polynomial of even degree.
Then,
The range of the function $f(x) = \frac{{x + 2}}{{|x + 2|}}$ is
If ${e^x} = y + \sqrt {1 + {y^2}} $, then $y =$