Given a function: ๐(๐ฅ) = ๐ฅ2 + 2.a. Does ๐(๐ฅ) has an inverse for all values of ๐ฅ
Question
Given a function:
Does have an inverse for all values of ?
Solution
The function f(x) = x^2 + 2 does not have an inverse for all values of x. This is because the function is not one-to-one, meaning that there are multiple values of x that can produce the same output.
For a function to have an inverse, it must be both one-to-one (each x-value corresponds to exactly one y-value) and onto (each y-value corresponds to at least one x-value). The function f(x) = x^2 + 2 is not one-to-one because, for example, both x = 2 and x = -2 produce the same output (y = 6).
Therefore, the function f(x) = x^2 + 2 does not have an inverse for all values of x.
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