Question

show that the function f:R->R given f(x)=x^3 is injective

Answer 1

Answer:

Here,

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<br>

<br> Let

<br> Then,<br>

<br>

<br> So, if

then

.<br>

Given function is injective(one-one).<

Step-by-step explanation:

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Answer 2

Answer:

method 1 :- Let x , y ∈ R such that f(x) = f(y)

x³ = y³

taking cube root both sides,

x = y , therefore f is one - one or injective mapping.

method 2 :- if any function f is strictly increasing or strictly decreasing in its domain then, f must be one - one or injective mapping.

it means, if differentiation of f = f' > 0 or f ' < 0 for all belongs to its domain.

then, f is one - one or surjective mapping.

Here, f(x) = x³

differentiate with respect to x

f'(x) = 3x² > 0 for all x belongs to R

then, f is one - one or injective mapping.

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