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…

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
  1. 1,2
  2. $-1,2$
  3. $-1,-2$
  4. $1,-2$

Solution

we have, $f(x)=2 x+3, g(x)=x^2+7$ $g(f(x))=g(2 x+3)=(2 x+3)^2+7=8$ $\Rightarrow \quad 4 x^2+9+12 x+7=8$ $\Rightarrow \quad 4 x^2+12 x+8=0$ $\Rightarrow \quad x^2+3 x+2=0$ $\Rightarrow \quad(x+1)(x+2)=0$ $\therefore \quad x=-1,-2$

Asked in: AP EAMCET 2003

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