NDA2023MathematicsFunctionsActual
A mapping f: A B defined as f(x)= 2 x+3 3 x+5 , x A . If f is to be onto, then what are A and B equal to?
Options
- AA=R - 5 3 and B=R - 2 3
- BA = R and B =B=R - 5 3
- CA=R - 3 2 and B = R 0
- DA=R - 5 3 and B=R 2 3
Correct answer
D. A=R - 5 3 and B=R 2 3
Step-by-step solution
f(x)= 2 x+3 3 x+5 Clearly for domain, 3 x+5 0 x - 5 3 Domain =A=R- - 5 3 for onto function, Range = Co-domain B= Range of fy= 2 x+3 3 x+5 3 x y+5 y=2 x+3 x(3 y-2)=3-5 yx= 3-5 y 3 y-2 Clearly, 3 y-2 0 y 2 3 B=R- 2 3