CAT 2021 Functions Question (Hard)

Question

For all real values of x, the range of the function f x is

Accepted Answer

We are given f x 2x 2 4x 9 . We need the range for all real . --- Step 1 Let y 2x 2 4x 9 Cross-multiply y 2x 2 4x 9 x 2 2x 4 Simplify 2y x 2 4y x 9y x 2 2x 4 Bring all terms to one side 2y - 1 x 2 4y - 2 x 9y - 4 0 For real , the discriminant must be non-negative . --- Step 2 Discriminant condition

CAT 2021

Quantitative

Functions

Hard

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

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