Question

Can someone rephrase this with different equations please I really need this!


Even if the inverses of both g(x) and f(x) are functions, the inverse of the sum of g(x) and f(x) may not be a function. As an example, I will use f(x) = 3x +2 and g(x) = 2x - 3. Both are one-to-one functions. The sum of f(x) and g(x) is 5x - 1. As 5x - 1 is also a one-to-one function, its inverse is a function as well. This example is in favor of the sum of two one-to-one function also being a one-to-one function. But take c(x) = (5x - 1)/ ((x/2) + 4 ) as another example. C(x) + f(x) is still a function, but the inverse of c(x) + f(x) is not. The inverse form does not pass the vertical line test in desmos. So, not every sum of two one-to-one functions is also a one-to-one function.

Answer 1

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