Question

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

Short answer

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

Step-by-step solution

Given Information :

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

To find the distances A and B :

The point ${y_k}^{*}$is given, we need to change the given function, role="math" localid="1654618022949" $y=f\left(x\right)$in terms of function in y, that is, role="math" localid="1654617969645" $x=f^{-1}\left(y\right)$.

The x - coordinate isrole="math" localid="1654618310732" $A=f^{-1}\left({y_k}^{*}\right)$and y - coordinate is$B={y_k}^{*}$.