Assertion \) defined by = \) \) is onto for all \) Reason For onto function codo

The function f(x)=tan^{-1}(x^2+x+a) has domain R and codomain [0,π/2). For a<1/4, the quadratic x^2+x+a has minimum a-1/4<0, so the range of the quadratic includes negative values. Since tan^{-1} is increasing, the range of f includes negative numbers (e.g., tan^{-1}(a-1/4)<0). Thus, f(x) takes values outside [0,π/2) for these a, so f is not even well-defined as a function to that codomain, let alone onto. Hence the Assertion is false. The Reason correctly states that onto implies codomain equals range, which is a true definition. Therefore, Assertion is incorrect but Reason is correct.