Question

If f : R → R defined by f(x) = x²+3 , then f is  (a)one-one onto (b) many-one onto (c) one-one but not onto (d) neither one-one nor onto​

Answer 1

Answer:

ANSWER

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.

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