Finding the Value of an Inverse Function – Step by Step

Full transcript

Today we're going to solve a function problem step by step, so don't worry if you're completely new to this — we'll break everything down together nice and simply. A function is just a machine — you put a number in, it does something to it, and spits a new number out. Here, our function is f of x equals k times the quantity two plus x. An inverse function is just the machine working backwards — instead of going in to get out, we start with the output and figure out what the input must have been. Our problem tells us that f-inverse of negative two equals negative three. This means that when the output of the inverse is negative three, the input was negative two — so f of negative three must equal negative two. So now we can write the equation f of negative three equals negative two, which means k times the quantity two plus negative three equals negative two. We just plugged negative three in for x. Inside the bracket, two plus negative three gives us negative one, so the equation becomes k times negative one equals negative two. Now we just solve for k by dividing both sides by negative one. Negative two divided by negative one gives us positive two, so k equals two! That's our final answer — k equals two. You just solved an inverse function problem, and now you know exactly how it works!