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If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x)=2 x+3$ and $g(x)=x^2+7$, then the values of $x$ such that $g(x)=x^2+7$, then the values of $x$ such that $g(f(x))=8$ are
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The correct answer is:
$-1,-2$
we have, $f(x)=2 x+3, g(x)=x^2+7$
$g(f(x))=g(2 x+3)=(2 x+3)^2+7=8$
$\Rightarrow \quad 4 x^2+9+12 x+7=8$
$\Rightarrow \quad 4 x^2+12 x+8=0$
$\Rightarrow \quad x^2+3 x+2=0$
$\Rightarrow \quad(x+1)(x+2)=0$
$\therefore \quad x=-1,-2$
$g(f(x))=g(2 x+3)=(2 x+3)^2+7=8$
$\Rightarrow \quad 4 x^2+9+12 x+7=8$
$\Rightarrow \quad 4 x^2+12 x+8=0$
$\Rightarrow \quad x^2+3 x+2=0$
$\Rightarrow \quad(x+1)(x+2)=0$
$\therefore \quad x=-1,-2$
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