Let f(x) = e^x – x and g(x) = x² – x, $$\forall $$ x $$ \in $$ R. Then the set of all x $$ \in $$ R, where the function h(x) = (fog) (x) is increasing, is :

Let f(x) = x² , x $$ \in $$ R. For any A $$ \subseteq $$ R, define g (A) = { x $$ \in $$ R : f(x) $$ \in $$ A}. If S = [0,4], then which one of the following statements is not true ?

The domain of the definition of the function

$$f(x) = {1 \over {4 - {x^2}}} + {\log _{10}}({x^3} - x)$$ is

If the function ƒ : R – {1, –1} $$ \to $$ A defined by
ƒ(x) = $${{{x^2}} \over {1 - {x^2}}}$$ , is surjective, then A is equal to