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Question
Mark the correct alternative in the following question:
Let f : R→ R be defined as, f(x) = \[\begin{cases}2x, if x > 3 \\ x^2 , if 1 < x \leq 3 \\ 3x, if x \leq 1\end{cases}\]
Then, find f( \[-\]1) + f(2) + f(4)
Options
9
14
5
none of these
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Solution
\[We have, \]
\[f\left( x \right) = \begin{cases}2x, if x > 3 \\ x^2 , if 1 < x \leq 3 \\ 3x, if x \leq 1\end{cases}\]
\[Now, \]
\[f\left( - 1 \right) + f\left( 2 \right) + f\left( 4 \right)\]
\[ = 3\left( - 1 \right) + 2^2 + 2\left( 4 \right)\]
\[ = - 3 + 4 + 8\]
\[ = 9\]
Hence, the correct alternative is option (a).
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