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

Answer 1

(c) −1, −2
f(x) = 2x + 3 and g(x) = x² + 7

$$\begin{gathered} g\left(f\right(x\left)\right)=8 \\ \Rightarrow {\left(f\left(x\right)\right)}^2+7=8 \\ \Rightarrow (2x+3{)}^2+7=8 \\ \Rightarrow x^2+3x+2=0 \\ \Rightarrow (x+2\left)\right(x+1)=0 \\ \Rightarrow x=-1,-2 \end{gathered}$$