Functions

If $f(x)=\log _e\left(6-\left|x^2+x-6\right|\right)$, then domain of $f(x)$ has how many integral values of $x$ ?

The range of the function $f(x)=\log _5\left(25-x^2\right)$ is

If $f(x)=\left(a-x^n\right)^{1 / n}$, where $a\gt0$ and $n$ is a positive integer, then $f[f(x)]$ is equal to

The number of solutions of the equation $9 x^2-18|x|+5=0$ belonging to the domain of definition of $\log _e\{(x+1)(x+2)\}$, is

If $f(x)=\cos \left[\pi^2\right] x+\cos \left[-\pi^2\right] x$, then

If $f(x+y)=f(x) \cdot f(y), f(3)=3, f^{\prime}(0)=11$, then $f^{\prime}(3)$ is equal to

Let $f(x)=\frac{1}{\sqrt{1+x^2}}$, then

If $f(x)=\frac{a^x+a^{-x}}{2}$ and $f(x+y)+f(x-y)$ $=k f(x) f(y)$, then $k$ is equal to

Let $f(x)=\sqrt{1+x^2}$, then

Let $f(x)$ is a polynomial function such that $f(x)+f\left(\frac{1}{x}\right)=f(x) \cdot f\left(\frac{1}{x}\right), x\gt0$ and $f(3)=10$, if $\int f(x) d x=g(x)+c$ and $g(1)=\frac{4}{3}$, then the value of $g(3)$ is

Let $f: R \rightarrow R$ be defined by $f(x)=\frac{x}{\sqrt{1+x^2}}$, then $(f \circ f \circ f)(x)$ is

The domain of the function $f(x)=\frac{\sin ^{-1}(3-x)}{\log (|x|-2)}$ is :