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NDA 2024

Exam: NDA
Year: 2024
Subject: Mathematics
Chapter: Functions

NDA 2024 · Mathematics · Functions

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

If

f(x)=4 x+1

and

g(x)=k x+2

such that

f {}^{\circ} g(x)=g {}^{\circ} f(x)

, then what is the value of

k ?

Options

A $7$
B $5$
C $4$
D $3$

Correct answer

A. $7$

Step-by-step solution

\begin{aligned} & \text{ Given, } f(x)=4 x+1, g(x)=k x+2 \\ & \text{fog }(x)=4(k x+2)+1=4 k x+9 \\ & \text{go } f(x)=k(4 x+1)+2=4 k x+k+2 \\ & \text{fog }(x)=g \text{ of }(x) \Rightarrow g=k+2 \Rightarrow k=7\end{aligned}

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