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(C) Given functions are $f(x) = 2x + 3$ and $g(x) = x^2 + 7$. We need to find $x$ such that $g(f(x)) = 8$. First,calculate the composite function $g(f

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$-1, -2$

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(C) Given functions are $f(x) = 2x + 3$ and $g(x) = x^2 + 7$. We need to find $x$ such that $g(f(x)) = 8$. First,calculate the composite function $g(f(x))$: $g(f(x)) = g(2x + 3) = (2x + 3)^2 + 7$. Set this equal to $8$: $(2x + 3)^2 + 7 = 8$ $(2x + 3)^2 = 1$ Taking the square root on both sides: $2x + 3 = 1$ or $2x + 3 = -1$ Case $1$: $2x = 1 - 3 = -2 \Rightarrow x = -1$. Case $2$: $2x = -1 - 3 = -4 \Rightarrow x = -2$. Thus,the values of $x$ are $-1$ and $-2$.

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x)=2x+3$ and $g(x)=x^2+7$,then the values of $x$ such that $g(f(x))=8$ are

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