THE FUCTION F: R= R , DEFINE AS F(X) =SIN (2X+3),IS NOTE 1-1 NOT ONTO HOW - Maths - Relations and Functions

Question

THE FUCTION F: R=>R , DEFINE AS F(X) =SIN (2X+3),IS

NOTE 1-1 NOT ONTO HOW

Md.Ashraf Khan · Accepted Answer

Dear StudentF:R→R  (Domain = R   and Co-domain=R)F(x) = sin(2x+3) = sin(θ)    {let 2x+3 = θ}We know that ;    -1≤sinθ≤1 i
e Range : [-1,1] which is                                ≠ co-domain(=R) of the given function ∴ sin(θ) is not ONTO  since it doesn't gives all elements of Co-domain(R) as output
<img alt="Image result for sine periodic" src=
"http://photos1%20blogger%20com/blogger/1071/3787/1600/PeriodicFunction%200%20gif">
Secondly sinθ is periodic i
e the values it gives repeat after a fixed interval of input-valueEx : sin(π2) = sin(5π2) = 1 thus, it gives same output for many input-values∴ It is not one-one