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A function f:R→R defined by f(x)=5x^4+2 is one – one but not onto.(a) True(b) FalseI have been asked this question in an international level competition.This key question is from Types of Functions topic in division Relations and Functions of Mathematics – Class 12

Answer»

Correct choice is (b) False

The explanation is: The above statement is false. f is neither one-one nor onto.

For one-one: CONSIDER f(x1)=f(x2)

∴ 5x1^4+2=5x2^4+2

⇒x1=± x2.

Hence, the function is not one – one.

For onto: Consider the real number 1 which lies in CO- domain R, and let \(x=(\FRAC{y-2}{5})^{\frac{1}{4}}\).

Clearly, there is no real value of x which lies in the domain R such that f(x)=y.

Therefore, f is not onto as every element LYING in the codomain must have a pre- image in the domain.



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