Find \(g(x)\)
🎥 Video Explanation
📝 Question
Given:
\[ f(x)=\sin^2 x \]
\[ g(f(x))=|\sin x| \]
Find \(g(x)\).
- (a) \(\sqrt{x-1}\)
- (b) \(\sqrt{x}\)
- (c) \(\sqrt{x+1}\)
- (d) \(-\sqrt{x}\)
✅ Solution
🔹 Step 1: Substitute \(f(x)\)
\[ g(\sin^2 x)=|\sin x| \] —
🔹 Step 2: Express RHS
\[ |\sin x|=\sqrt{\sin^2 x} \]
—🔹 Step 3: Compare
\[ g(\sin^2 x)=\sqrt{\sin^2 x} \]
So:
\[ g(x)=\sqrt{x} \] —
🔹 Final Answer
\[ \boxed{\text{Option (b)}} \]