For every twice differentiable function $$f:R \to [ - 2,2]$$ with $${(f(0))^2} + {(f'(0))^2} = 85$$, which of the following statement(s) is(are) TRUE?

Let f : R $$ \to $$ R and g : R $$ \to $$ R be two non-constant differentiable functions. If f'(x) = (e^{(f(x) $$-$$ g(x))}) g'(x) for all x $$ \in $$ R and f(1) = g(2) = 1, then which of the following statement(s) is (are) TRUE?

Let f : [0, $$\infty $$) $$ \to $$ R be a continuous function such that

$$f(x) = 1 - 2x + \int_0^x {{e^{x - t}}f(t)dt} $$ for all x $$ \in $$ [0, $$\infty $$). Then, which of the following statement(s) is (are) TRUE?

The value of $${({({\log _2}9)^2})^{{1 \over {{{\log }_2}({{\log }_2}9)}}}} \times {(\sqrt 7 )^{{1 \over {{{\log }_4}7}}}}$$ is ....................