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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Functions

NDA 2022 · Mathematics · Functions

If f(x)=4 x+1 and g(x)=k x+2 such that f o g(x)=gof(x) , then what...

If f(x)=4x+1f(x)=4 x+1 and g(x)=kx+2g(x)=k x+2 such that fog(x)=gof⁡(x)f o g(x)=\operatorname{gof}(x), then what is the value of kk ?

Options

  1. A77
  2. B55
  3. C44
  4. D33

Correct answer

A. 77

Step-by-step solution

 Given that f(g(x))=g(f(x))⇒(f(kx+2)=g(4x+1)⇒4(kx+2)+1=k(4x+1)+2⇒4kx+9=4kx+k+2⇒k=7\begin{aligned} & \text{ Given that } f(g(x))=g(f(x)) \\ & \Rightarrow \quad(f(k x+2)=g(4 x+1) \\ & \Rightarrow 4(k x+2)+1=k(4 x+1)+2 \\ & \Rightarrow \quad 4 k x+9=4 k x+k+2 \Rightarrow k=7\end{aligned}
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