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If $f(x)=a x+b$, where $a$ and $b$ are integers, $f(-1)=-5$ and $f(\beta)=3$, then $a$ and $b$ are respectively
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The correct answer is:
$2,-3$
Given, $f(x)=a x+b$, where $a$ and $b$ are
integers, $f(-1)=-5$ and $f(3)=3$
We have, $f(x)=a x+b$
Put, $x=-1$ in above equation, we get
$\begin{aligned} f(-1) & =a(-1)+b \\ -5 & =-a+b\end{aligned}$
Now, $f(3)=3$
$3=3 a+b$
From Eqs. (i) and (ii), we get
$a=2, b=a-5=2-5=-3$
integers, $f(-1)=-5$ and $f(3)=3$
We have, $f(x)=a x+b$
Put, $x=-1$ in above equation, we get
$\begin{aligned} f(-1) & =a(-1)+b \\ -5 & =-a+b\end{aligned}$
Now, $f(3)=3$
$3=3 a+b$
From Eqs. (i) and (ii), we get
$a=2, b=a-5=2-5=-3$
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