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Show that the function f: R->R given by...

Show that the function `f: R->R` given by `f(x)=x^3`is injective.

Text Solution

Verified by Experts

Here, `f(x) = x^3`
`:. f(x_1) = x_1^3`
`f(x_2) = x_2^3`
Let `f(x_1) = f(x_2)`
Then,
`x_1^3 = x_2^3`
`=>x_1 = x_2`
So, if `f(x_1) = f(x_2),` then `x_1 = x_2`.
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