Question

If \(f:\mathbb{R}\to\mathbb{R}\) and \(g:\mathbb{R}\to\mathbb{R}\) be functions such that \(f(x)=\cos x\) and \(g(x)=3x^3\), then find \(f\circ g\).

Hint:

\((f\circ g)(x)=f(g(x))\): replace the input of \(\cos\) with \(3x^3\).

Answer 1

Step 1: Understanding the Concept:
\((f\circ g)(x)=f(g(x))\) means: first apply \(g\), then feed that output into \(f\).

Step 2: Applying g first:
\(g(x)=3x^3\).

Step 3: Feeding into f:
\(f(g(x))=f(3x^3)=\cos(3x^3)\), since \(f\) just takes cosine of whatever is fed in.

Final Answer:
\((f\circ g)(x)=\boxed{\cos(3x^3)}\).