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Show that the Function F: R → R Given by F(X) = X3 is Injective. - CBSE (Commerce) Class 12 - Mathematics

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Question

Show that the function fR → R given by f(x) = x3 is injective.

Solution

fR → R is given as f(x) = x3.

Suppose f(x) = f(y), where xy ∈ R.

⇒ x3 = y3 … (1)

Now, we need to show that x = y.

Suppose x ≠ y, their cubes will also not be equal.

⇒ x3 ≠ y3

However, this will be a contradiction to (1).

∴ x = y

Hence, f is injective.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 1: Relations and Functions
Q: 5 | Page no. 29
Solution Show that the Function F: R → R Given by F(X) = X3 is Injective. Concept: Types of Functions.
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