CAT 2025 Slot 3 QA Question 3

Multiple choice (+3 / −1) · Algebra · Functions · Try it, then check the answer and solution below.

CAT 2025 Slot 3QAAlgebra • FunctionsModerate

For real values of

x , the range of the function

f(x)=

\frac{2x-3}{2x^2+4x-6}

⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution

Official Convenor Answer Key: B

Answer and solution

Answer: B) $\left(-\infty,\frac{1}{8}\right]\cup\left[\frac{1}{2},\infty\right)$

📌 Core Concept & Formula

To determine the range of a rational function

f(x) = \frac{p(x)}{q(x)} , set

y = f(x)

and solve for

in terms of

. The function will have real values if the discriminant of the resulting quadratic equation is non-negative. The discriminant

of a quadratic equation

ax^2 + bx + c = 0$ is given by \( D = b^2

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