Question

10.
The function f: R R defined as f(x) = (x - 1)(x-2)(x-3) is
(1) One-one but not onto
(2) Onto but not one-one
(3) Both one-one and onto
(4) Neither one-one nor onto
nd complex mumhor​

Answer 1

Answer:

b) Onto but not one one

Step-by-step explanation:

f(x)=(x−1)(x−2)(x−3)

one−one test:

⇒ f(1)=(1−1)(1−2)(1−3)=0

⇒ f(2)=(2−1)(2−2)(2−3)=0

⇒ f(3)=(3−1)(3−1)(3−3)=0

⇒ f(1)=f(2)=f(3)=0

We can see, 1,2,3 has same image 0.

∴ f is not one-one.

onto test:

Let y be an element in the co-domain R, such that

y=f(x)

⇒ y=(x−1)(x−2)(x−3)

Since, y∈R and x∈R.

∴ f is onto.