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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
Options
(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
\[g(f(x)) = 8\]
\[ \Rightarrow \left( f(x) \right)^2 + 7 = 8\]
\[ \Rightarrow (2x + 3 )^2 + 7 = 8\]
\[ \Rightarrow x^2 + 3x + 2 = 0\]
\[ \Rightarrow (x + 2)(x + 1) = 0\]
\[ \Rightarrow x = - 1, - 2\]
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