Question

a function f: R-R is Defined by F(x)=2x^2 is the function f is one one and onto justify your answer?

Answer 1

funtion is not one one and onto.

range of the function [ 0, ∞)

so function is into and

at

x = 1 & x = -1

y = 2 ( which gives same value )

so funtion is not one - one.

now we can say that function is many one & into.

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Hope it will help you.✌✌

Answer 2

Answer:

The function is not one one but onto.

Step-by-step explanation:

check one one :

f(x1) = f(x2)

=>2x²1 = 2x²2

=>x1 = ±x2

Thus , the function f is not one one .

check onto :

f(x) = 2x²

=> y = 2x²

=> x = √y/2

Therefore , f(√y/2) = 2(√y/2)² = y

=> f(x) = y

Thus , the function is onto.