Functions
Composite and Bijective Functions
JEE Main 2024
Grade 12
Question:
If $f(x) = \frac{4x + 3}{6x - 4}$, $x \neq \frac{2}{3}$, and $(f \circ f)(x) = g(x)$, then $g$ is:
(1) one-one but not onto
(2) onto but not one-one
(3) neither one-one nor onto
(4) bijective with $g(x) = x$
Step-by-Step Solution
Key Concept: Compute $f(f(x))$ by substituting $f(x)$ into $f$. You should find the composition simplifies to something very clean.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (4)