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

विकल्प

• (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

\[g(f(x)) = 8\]

\[ \Rightarrow \left( f(x) \right)^2 + 7 = 8\]

\[ \Rightarrow (2x + 3 )^2 + 7 = 8\]

\[ \Rightarrow x^2 + 3x + 2 = 0\]

\[ \Rightarrow (x + 2)(x + 1) = 0\]

\[ \Rightarrow x = - 1, - 2\]