Let $\phi (x) = (x) + {2^{\log _x^3}} - {3^{\log _x^2}}$ then

If $f$ is an even function defined on the interval $(-5, 5),$ then four real values of $x$ satisfying the equation $f(x) = f\left( {\frac{{x + 1}}{{x + 2}}} \right)$ are

If $f(x)$ be a polynomial function satisfying $f(x).f (\frac{1}{x}) = f(x) + f (\frac{1}{x})$  and $f(4) = 65$ then value of $f(6)$ is

Let $f : R \rightarrow R$ be a function such that $f(x)=\frac{x^2+2 x+1}{x^2+1}$. Then

Let ${f_k}\left( x \right) = \frac{1}{k}\left( {{{\sin }^k}x + {{\cos }^k}x} \right)\;,x \in R$ and $k \ge 1$, then ${f_4}\left( x \right) - {f_6}\left( x \right)$ is equal to

The domain of the function $f(x) = {\sin ^{ - 1}}[{\log _2}(x/2)]$ is