NDA2010MathematicsFunctionsActual
The function f(x)= x x^2+1 from R to R is
Options
- AOne-one as well as onto
- BOnto but not one-one
- CNeither one-one nor onto
- DOne-one but not onto
Correct answer
C. Neither one-one nor onto
Step-by-step solution
aligned & f(x)= x x^2+1 & f (x₁ )= x₁ x₁^2+1 , f (x₂ )= x₂ x₂^2+1 & f (x₁ )=f (x₂ ) aligned aligned & x₁ x₁^2+1 = x₂ x₂^2+1 & or x₁ x₂^2+x₁=x₂ x₁^2+x₂ & or x₁ x₂^2-x₂ x₁^2=x₂-x₁ & x₁ x₂=1 aligned f is neither one-one nor onto.