Functions
Composite Functions
JEE Main 2019
Grade 12
Question:
If $g(x) = x^2 + x - 1$ and $(g \circ f)(x) = 4x^2 - 10x + 5$, then $f\left(\frac{5}{4}\right)$ equals:
(1) $-\frac{1}{2}$
(2) $\frac{3}{2}$
(3) $-\frac{3}{2}$
(4) $\frac{1}{2}$
Step-by-Step Solution
Key Concept: Try $f(x) = ax+b$ (linear). Expand $g(f(x))$ and match with $4x^2 -10x+ 5$. Two equations in $a$ and $b$ — solve and substitute.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)