Question

Inverse


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Answer 1

It looks like we're viewing the graph of the equation y = x^2 + 1, lets try to find the inverse and see if any of those options match up to what we get!
So let's switch the variables and then solve for y...
\[x = y^{2} + 1\] which becomes
\[y = \pm \sqrt{x - 1}\]
Hmm....to me, that doesn't quite look like a function!

Answer 2

The inverse of a function is always the same shape, reflected across the line y = x.

For example, the plot in this problem is an upward opening parabola such as \(y=x^2\). The inverse can be found by solving for x, then swapping x and y:\[y=x^2\]\[\pm\sqrt{y} = x\]\[y = \pm\sqrt{x}\]
The two graphed together look like the attached diagram.

Answer 3

Now, if you can draw a vertical line at any value of x and cross the curve more than once, you do not have a function, because a function has only 1 value of y for any value of x.

Answer 4

Both answers are perfect