f : R → R : f(x) = x^2 is A. one - one and onto B. one - one and into C. many - one and onto D. many - one and into

Question

Mark (√) against the correct answer in the following: 

f : R → R : f(x) = x² is 

A. one - one and onto 

B. one - one and into 

C. many - one and onto 

D. many - one and into

Answer 1

Correct Answer is (D) many - one into

f(x) = x²

⇒y = x²

in this range the lines cut the curve in 2 equal valued points of y, therefore, the function f(x) = x² is many - one .

Range of f(x) = (0,∞)≠R(codomain)

∴f(x) is into

∴ f : R → R: f(x) = x² is many - one into