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.

Question

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.

Knowee AI · Accepted Answer

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.

Given a function: 𝑓(𝑥) = 𝑥2 + 2.a. Does 𝑓(𝑥) has an inverse for all values of 𝑥

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Given a function:

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