The domain of the definition of the function $y(x)$ given by the equation $2^x+2^y=2$ is

The function $f: R \rightarrow R$ is defined by $f(x) = \cos^2 x + \sin^4 x$ for $x \in R$. Then $f(R)$ is equal to:

If $f:[2, \infty) \rightarrow B$ defined by $f(x)=x^2-4x+5$ is a bijection, then $B$ is equal to

Let $A = \{-4, -2, -1, 0, 3, 5\}$ and $f: A \rightarrow R$ be defined by $f(x) = \begin{cases} 3x - 1 & \text{for } x > 3 \\ x^2 + 1 & \text{for } -3 \leq x \leq 3 \\ 2x - 3 & \text{for } x < -3 \end{cases}$. Then the range of $f$ is

Range of the function $f(x) = \sin^2(x^4) + \cos^2(x^4)$ is

Domain of the function $f(x) = \frac{x^2 - 3x + 2}{x^2 + x - 6}$ is