Question Video: Evaluating Expressions Involving Composite Functions | Nagwa Question Video: Evaluating Expressions Involving Composite Functions | Nagwa

# Question Video: Evaluating Expressions Involving Composite Functions Mathematics

Use the table to evaluate π(π(2)) and π(π(1)).

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### Video Transcript

Use the table to evaluate π of π of two and π of π of one.

Letβs have a look at this table and understand what it is telling us first. There are four values of π₯: one, two, three, and four. The next column tells us the values of the function π for each of these values of π₯. For example, π of three is equal to nine. The final column tells us the values of π for these same values of π₯. For example, π of four is equal to eight.

In the question, weβre asked to determine π of π of two and π of π of one. So, letβs think about what each of these means. π of π of π₯ is the composite function we get when we take an input, apply the function π first, and then apply the function π to the result. So, for π of π of two, weβre taking the input value two, applying π, and then applying π to whatever value we have.

Letβs look at the table. We can see that π of two is equal to four. To find π of π of two, we need to take this value as the input to the function π. So, π of π of two is equal to π of four. Looking at the table again, this time the second column, we see that π of four is equal to 12. So, we found the first answer. π of π of two is equal to 12.

The second thing weβre asked to evaluate is π of π of one. Now this time the functions have been composed in the opposite order. Weβre applying the function π first and then applying the function π to the result. Starting with an input value of one then, we see from the table that π of one is equal to three. Then, to find π of π of one, we take this value of three as the input to the function π. π of π of one is equal to π of three. Returning to the table and looking in the third column, we see that π of three is equal to six.

So, weβve answered both parts of the question. π of π of two is equal to 12, and π of π of one is equal to six.