Functions
Composite Functions
JEE Main 2022
Grade 12
Question:
Let $f(x) = \frac{x - 1}{x + 1}$, $x \neq 0, -1$, and $f^{n+1}(x) = f(f^n(x))$. Then $f^6(6) + f^7(7)$ equals:
(1) $\frac{3}{2}$
(2) $\frac{1}{2}$
(3) $-\frac{3}{2}$
(4) $-\frac{1}{2}$
Step-by-Step Solution
Key Concept: Compute $f^2(x), f^3(x), f^4(x)$ and spot the period. Use the period to reduce the exponents, then substitute $x = 6$ and $x = 7$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)