Find the Values of \( x \) Such That \( g(f(x))=8 \)
If
\[ f(x)=2x+3 \]
and
\[ g(x)=x^2+7 \]
then the values of \(x\) such that
\[ g(f(x))=8 \]
are
(a) \(1,2\)
(b) \(-1,2\)
(c) \(-1,-2\)
(d) \(1,-2\)
\[ g(f(x))=(2x+3)^2+7 \]
Given,
\[ (2x+3)^2+7=8 \]
\[ (2x+3)^2=1 \]
\[ 2x+3=\pm1 \]
If
\[ 2x+3=1 \]
\[ x=-1 \]
If
\[ 2x+3=-1 \]
\[ x=-2 \]
Therefore,
\[ \boxed{\text{Correct Answer: (c)}} \]