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Mathematics
Let f ( x ) = { 6 x 3 , x 5 x 2 , x > 5 f(x)={[6x-3","x <= -5],[],[-x^(2)","x > -5]:}. Find f ( 3 ) , f ( 5 ) f(-3),f(-5), and f ( 6 ) f(-6).
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For f ( 3 ) f(-3), we use the first case since 3 5 -3 <= -5:
f ( 3 ) = 6 ( 3 ) 3 = 18 3 = 21 f(-3)=6(-3)-3=-18-3=-21
For f ( 5 ) f(-5), we could use either case since 5 -5 is on the boundary, but we’ll use the first case:
f ( 5 ) = 6 ( 5 ) 3 = 30 3 = 33 f(-5)=6(-5)-3=-30-3=-33
For f ( 6 ) f(-6), we use the second case since 6 > 5 -6 > -5:
f ( 6 ) = ( 6 ) 2 = 36 f(-6)=-(-6)^(2)=-36
Therefore, f ( 3 ) = 21 f(-3)=-21, f ( 5 ) = 33 f(-5)=-33, and f ( 6 ) = 36 f(-6)=-36.
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