if A=[0,π/6,π/4,π/3,π/2] and F:A➡️B is a surjection defined by f(x)=cosx,then find B
Answers (2)
26th Oct, 2021
Hello student ,
f : A → B is surjection and f(x) = cos x.
Now B = f(A)
A = {0, pi/6 , pi/4 , pi/3 , pi/2}
f(0) = cos(0) = 1
f( pi/6 ) = cos( pi/6) = sqrt of 3 / 2
f( pi/4 ) = cos( pi/4) = sqrt of 1/2
f( pi/3) = cos( pi/3) = 1/2
f( pi/2) = cos( pi/2) = 0
Therefore B = f(A) = {1 , sqrt of 3 /2 , sqrt of 1 /2 , 1/2 , 0 }
Comments (0)
26th Oct, 2021
Hi aspirant,
A surjective function is a function whose image is equal to its co-domain. Also, the range, co-domain and the image of a surjective function are all equal. So every element in A will have a value defined by f(x) in B.
So results are cos0=1, cos pi/6= √3/2, cos pi/4= 1/√2, Cos pi/3= 1/2 and cos pi/2= 0
Hope it helps!!
Comments (0)
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