Question

Look at the function you wrote for question 5. Does this function have an inverse? If so, what is it? Is the inverse a function? A) Yes, the inverse is a function. B) No, it does not have an inverse. C) Yes, the inverse is not a function. D) No, it has an inverse that is a function.

Answer 1

In general, a function has an inverse if it is a bijection, meaning it is both injective (one-to-one) and surjective (onto). The inverse of a function swaps each output with its corresponding input. If the function's inverse passes the vertical line test, it can be considered a function, meaning there's only one output for each input.

Step-by-step explanation:

Without knowing the specific function from question 5, I can't say definitively whether it has an inverse or whether that inverse is a function. However, in general, a function has an inverse if it is a bijection, meaning it is both injective (or one-to-one) and surjective (or onto). The inverse of a function essentially flips the function around the line y=x, swapping each output with its corresponding input.

If a function's inverse passes the vertical line test (i.e., any vertical line only intersects the graph at most one point), then it can be considered a function. In other words, for every single input (x-value), there's only one output (y-value), which defines a function.

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