The input values are the x values. The output values for the inverse g function are shown in the third row. For example, the input x = -4 leads to a g inverse value of 10. See column 1.
When we find the original g(x) function, we swap the two rows mentioned. The inputs are now the bottom row values and the outputs are the x values.
We can see that the input x = 10 leads to y = -4 and y = 5 at the same time.
Therefore g(x) is NOT a function.
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At the same time,
The inverse of h(x) is NOT a function
Why not? Because we have the same issue as before. This time focus on the first two rows. The second row becomes the input values. We have the input x = 5 lead to y = -4 and y = -2 simultaneously.