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TS EAMCET · Maths · Functions

If \(f(x)\) and \(g(x)\) are two real valued functions such that \(f(x)=3 x-2\) and \(g(x)=x^2+2\) then \([(g \circ f)+(f \circ g)](x)=\)

  1. A \(2 g(x)+2 f(x)\)
  2. B \(12 g(x)-4 f(x)-22\)
  3. C \(3 g(x)+f(x)-2\)
  4. D \(2 f(x)+4 g(x)-32\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(12 g(x)-4 f(x)-22\)

Step-by-step Solution

Detailed explanation

\(f(x)=3 x-2\) \(g(x)=x^2+2\) \(\begin{aligned} & g \circ f(x)=g[f(x)]=f(x)^2+2 \\ & \& f \circ g(x)=f[g(x)]=3[g(x)]-2 \\ & (g \circ f+f \circ g)(x)=f(x)^2+2+3[g(x)]-2\end{aligned}\)…