Question Video: Finding the Value of an Inverse Function Mathematics • Higher Education

Let 𝑔 be the inverse of 𝑓. Using the table below, find 𝑔′(0).

01:07

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 π‘₯ 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 π‘₯ 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.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.