Video Transcript
Let 𝑔 be the inverse of 𝑓. Using the table below, find 𝑔
prime of zero.
In order to find 𝑔 prime of zero,
we’ll be using the formula for finding the derivative of an inverse of a
function. Which tells us that 𝑔 prime of 𝑦
is equal to one over 𝑓 prime of 𝑔 of 𝑦. We’re trying to find 𝑔 prime of
zero. So we can substitute in zero for
𝑦. This gives us that 𝑔 prime of zero
is equal to one over 𝑓 prime of 𝑔 of zero. From the table, we can see that
when 𝑥 is equal to zero, 𝑔 is equal to negative one. And so, we have that 𝑔 of zero is
equal to negative one. Which we can substitute in to give
us that 𝑔 prime of zero is equal to one over 𝑓 prime of negative one.
And now, we can simply read 𝑓
prime of negative one off from the table. Since when 𝑥 is equal to negative
one, 𝑓 prime is equal to one-third. Giving us that 𝑓 prime of negative
one is equal to one-third. And again, this can be substituted
in. And so, we will obtain that 𝑔
prime of zero is equal to the reciprocal of one-third. And here, we reach our solution of
three.
