# Question Video: Evaluating a an Evaluation of a Point of a Piecewise Function Mathematics

Consider the function π(π₯) = π₯ + 4 if π₯ > 4, π(π₯) = 2π₯ if β1 β€ π₯ β€ 4, and π(π₯) = β3 if π₯ < β1. Find π[π(2)].

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### Video Transcript

Consider the function π of π₯ is equal to π₯ plus four if π₯ is greater than four, two π₯ if π₯ is greater than or equal to negative one and less than or equal to four, and negative three if π₯ is less than negative one. Find π of π of two.

π of π of two is a composite function. Itβs a function of a function. Weβre going to begin by looking at the inner function first, so weβre going to begin by thinking about π of two. Now, our π of π₯ is a piecewise function, and itβs defined by different functions on different intervals of π₯. Weβre told that when π₯ is greater than four to use the function π₯ plus four. When π₯ is between and including negative one and four, we use the function two π₯. And when π₯ is less than negative one, we use the function π of π₯ equals negative three. Two, of course, lies between negative one and four, and so weβre going to use the second part of our function. That is, when π₯ is equal to two, π of π₯ is equal to the function two π₯.

And so, π of two is found by substituting two into this equation. We get two times two, which is four. So we found π of two; itβs four. If we replace π of two with its value of four, we see that we now need to evaluate π of four. And we need to be really careful here. Weβre actually still using this second part of the function. And this is because we only use the first part of the function when π₯ is strictly greater than four. When itβs less than or equal to four, we use the function two π₯. And so once again, we substitute our value of π₯ into the function π of π₯ equals two π₯, so itβs two times four which is equal to eight. Given our piecewise function, π of π of two is eight.