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Question
Let f : R → R, g : R → R be two functions defined by f(x) = x2 + x + 1 and g(x) = 1 − x2. Write fog (−2).
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Solution
\[\left( fog \right)\left( - 2 \right) = f \left( g \left( - 2 \right) \right)\]
\[ = f\left( 1 - \left( - 2 \right)^2 \right)\]
\[ = f\left( - 3 \right)\]
\[ = \left( - 3 \right)^2 + \left( - 3 \right) + 1\]
\[ = 9 - 3 + 1\]
\[ = 7\]
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