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A function f:R→R is defined by f(x)=5x^3-8. The type of function is _________________

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A function f:R→R is defined by f(x)=5x^3-8. The type of function is _________________

(a) one -one

(b) onto

(c) many-one

(d) both one-one and onto

The question was asked in unit test.

This interesting question is from Types of Functions topic in chapter Relations and Functions of Mathematics – Class 12

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Right answer is (c) many-one

Easy explanation: The above is a many -one function.

Consider f(x1)=f(x2)

∴5x1^3-8=5x2^3-8

5x1^3=5x2^3

⇒x1 = ±x2. Hence, the function is many – one.

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