Calculate the inverse function of a tangent to a graph without using the inverse function of the graph?
Hello, in task c) I have to specify the inverse function of the tangent t to f(t) without using the inverse function of f(t).
My first thought was to simply reverse the tangent equation. It was correct, but it wasn't listed as another option. What I don't understand is how to determine the slope of the inverse function of t.
It says this here:
But when I plug in the points (0|3/8) and (4|4), the result is always wrong, regardless of whether I have y at the bottom and y at the top, regardless of whether I use x as y and y as x, I always get the wrong result. So I was wondering if someone could explain the step for calculating the gradient to me again?
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The point is also wrong. From the axis section of the tangent, the zero point of the tangent to the reversing function is changed during the reflection at the angle halving:
Axle section of the tangent:
The tangent to the reversing function thus has the zero point N(5/2 | 0) and the tangent equation results from the two points P(4|4) and N(5/2| 0)
So the tangent he reverse function has the equation:
Sketch: