Question:
If f : R → R and g : R → R are defined by f(x) = 2x + 3 and g(x) = x2 + 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
Solution:
(c) −1, −2
f(x) = 2x + 3 and g(x) = x2 + 7
$g(f(x))=8$
$\Rightarrow(f(x))^{2}+7=8$
$\Rightarrow(2 x+3)^{2}+7=8$
$\Rightarrow x^{2}+3 x+2=0$
$\Rightarrow(x+2)(x+1)=0$
$\Rightarrow x=1 \mid=1,-2$