Question

If \(f(x) = \frac{1-x}{1+x}\), then \(f(f(cosx)) =\)

• A. \(cosx\)
• B. \(x\)
• C. \(tan\frac{x}{2}\)
• D. \(cos\frac{x}{2}\)

Hint:

From AB = C, the inverse of B is C inverse times A.

Answer 1

The Correct Option is A

Step 1: Find B itself:
$|A| = 7$, $A^{-1} = \frac17\begin{bmatrix}2 & -1\\ 1 & 3\end{bmatrix}$. So $B = A^{-1}C = \frac17\begin{bmatrix}14 & 0\\ 7 & 21\end{bmatrix} = \begin{bmatrix}2 & 0\\ 1 & 3\end{bmatrix}$.

Step 2: Invert B:
$|B| = 6$, so $B^{-1} = \frac16\begin{bmatrix}3 & 0\\ -1 & 2\end{bmatrix}$. Option (B).

Final Answer:
Option (B). \[ \boxed{\frac{1}{6}\begin{bmatrix}3 & 0\\ -1 & 2\end{bmatrix}} \]