CAT (QA) PYQs

For all real values of x, the range of the function f(x) = $\frac{x^2+2x+4}{2x^2+4x+9}$ is

If $f(x)=x^{2}-7 x$ and $g(x)=x+3$, then the minimum value of $f(g(x))-3 x$ is

Suppose $f(x, y)$ is a real valued function such that $f(3x + 2y, 2x- 5y) = 19x$, for all real numbers $x$ and $y$. The value of $x$ for which $f(x, 2x) = 27$, is