Let f(x) = l (sinx) - 1/2 l. <--- absolute value of sinx - 1/2

Question

The maximum value attained by f is.

Answer 1

Range of sin ( x ) = [ -1 , 1 ]

When sin ( x ) = - 1 then:

abs ( sin ( x ) - 1 / 2 ) = abs ( - 1 - 1 / 2 ) = abs ( - 1.5) = + OR - 1.5

When sin ( x ) = 1 then:

abs ( sin ( x ) - 1 / 2 ) = abs ( 1 - 1 / 2 ) = abs ( 0.5) = + OR - 0.5

The maximum value = 1.5

Answer 2

Correction:

abs ( - 1.5) = 1.5

abs ( 0.5) = 0.5