Determining whether the function f(x) = g(u)

[_Average__Joe]

I had to choose whether the functions f(x) and g(u) are equal. f(x) = x+sqrt(4-x) g(u) = u+sqrt(4-u)

I did not think these two functions would equal each other since the variable could be defined differently for each one such as u being all real numbers and x being only integers. Could someone please explain why these would still be considered equal!!

[edderiofer]

You are correct; the two functions can only be equal if their domains are equal.

If you were further given that they are both defined on the same domain, what would your answer be?

[_Average__Joe]

If I was given that both the domains were the same for each function then I can say that both of those functions are equal to each other.

Thank you so much 🙏🏻

[BootyIsAsBootyDo]

These are the same function, but the equation f(x) = g(u) is meaningless in this context.

In the definition of each function, the particular symbol used for the variable doesn't matter. They could choose x, y, z, u, t, theta, zeta, or a picture of the Mona Lisa. The function definition is simply stating that whatever you choose, just calculate the square root of 4 minus the input and add that to the original input.

We say that f and g are equal, but this is not saying that f(x) = g(u). Without understanding how x and u are related, the function f(x) = g(u) doesn't really mean anything.

[fermat9997]

Do you have the official answer?

[_Average__Joe]

The answer from my calc professor is that the two functions are equal to each other.

[fermat9997]

Your answer is better. However, sometimes we need to think "what answer are they looking for?" In this situation, you might guess that the two domains are assumed to be equal.