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A day full of math games & activities. Find one near you.
Show that function f: R → R be defined by f (x) = x3 is injective
Solution:
In mathematics, an injective function ( or one-to-one function) is a function f such that maps distinct elements to distinct elements
that is, f(x1) = f (x2)
⇒ x1 = x2
f : R → R be defined by
f (x) = x3
For one-one:
f (x) = f (y) where x, y ∈ R
x3 = y3 .... (1)
We need to show that x = y
Suppose x is not equal to y, their cubes will also not be equal.
⇒ x3 ≠ y3
This will be a contradiction to (1).
Therefore,
x = y.
Hence, f is injective
NCERT Solutions for Class 12 Maths - Chapter 1 Exercise ME Question 5
Show that function f: R → R be defined by f (x) = x3 is injective
Summary:
Here we have concluded that function f: R → R be defined by f (x) = x3 is injective
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