Q. 10 - Calculus

Question

For the figure, write the distances A and B in terms of $f$ or $f^{-1}$ and the point ${y_k}^{*}$ :

Step-by-Step Solution

Answer

$A={f^{-1}( y_k}^{*})$ and $B={y_k}^{*}$.

Step 1: Given Information :

In the figure, the function $y=f\left(x\right)$ and a point ${y_k}^{*}$ are given.

Step 2: To find the distances A and B :

The point ${y_k}^{*}$ is given, we need to change the given function, $y=f\left(x\right)$ in terms of function in y, that is, $x=f^{-1}\left(y\right)$.

The x - coordinate is  $A= f^{-1}\left({y_k}^{*}\right)$ and y - coordinate is $B= {y_k}^{*}$.