Question

6. Find subsets A and B of R, with A as large as possible, such that f : A + B defined by f(x) = x2 + 4x - 7 is one-to-one and onto. ​

Answer 1

Explanation:

Let (a

1

,b

1

),(a

2

,b

2

)∈A×B such that f(a

1

,b

1

)=f(a

2

,b

2

).

⇒(b

1

,a

1

)=(b

2

,a

2

)

⇒b

1

=b

2

) and (a

1

=a

2

)

⇒(a

1

,b

1

)=(a

2

,b

2

)

∴f is one-one.

Now, let (b,a)∈B×A be any element.

Then, there exists (a,b)∈A×B such that

f(a,b)=(b,a). [By definition of f]

∴f is onto.

Hence, f is bijective.