Functions Test ...

If $$f:R\rightarrow S$$ defined by
$$f(x)=4\sin { x } -3\cos { x } +1$$ is onto, then $$S$$ is equal to

Domain of definition of the function $$f(x) = \dfrac{3}{4 - x^2} + \log_{10} (x^3 - x),$$ is 

A function f has domain [-1, 2] and range [0, 1]. The domain and range respectively of the function g defined by g (x) = 1 -f (x+1) is 

The domain of definition of the function $$\displaystyle f(x) = \sqrt{-cos x} + \sqrt{sin x}$$ is:

Let for $$a \neq a_{1} \neq 0,\ f(x)=ax^{2}+bx+c,\ g(x)=a_{1}x^{2}+b_{1}x+c_{1}$$ and $$p(x)=f(x)-g(x)$$. If $$p(x)=0$$ only for $$x=-1$$ and $$p(-2)=2$$, then the value of $$p(2)$$ is

Let $$f(-2, 2)\rightarrow(-2, 2)$$ be a continuous function given $$f(x)=f{(x}^{2})$$. Given $$f(0)=\dfrac{1}{2}$$ then the $$4f(\dfrac{1}{2})$$

Given that $$f'(x) > g'(x)$$ for all real x, and $$f(0) = g(0)$$. Then $$f(x) < g(x)$$ for all x belongs to

If $$ \phi (x) = 3
f(\frac{x^2}{3} ) + f(3-x^2) \forall x \in (3,4)$$ where  $$f(x) >0 \forall  x (-3,4)$$ then $$\phi (x)$$ is ____________.

The domain of the function $$ f(x) = log_{1/2}\Big(-log_2(1+\frac{1}{\sqrt{4}})-1\Big)$$

Let f(x) and g(x) be the differentiable functions for $$1\le x\le 3$$ such that f(1)=2=g(1) and f(3)=10. Let there exist exactly one real number $$cE (1,3)$$ such that 3f'(c)=g'(c), then the value of g(3) must be