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

Question

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

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Answer

f: R → R is given as f(x) = x³
Suppose f(x) = f(y), where $\text{x},\text{y}\in\text{R}.$
⇒ x³ = y³...(1)
Now, we need to show that x = y.
Suppose $\text{x}\neq\text{y},$ their cubes will also not be equal.
$\Rightarrow\text{x}^3\neq\text{y}^3$
However, this will be a contradiction to (1).
$\therefore$ x = y
Hence, f is injective.

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