Question Video: Finding an Algebraic Expression for the Composition of Two Functions | Nagwa Question Video: Finding an Algebraic Expression for the Composition of Two Functions | Nagwa

# Question Video: Finding an Algebraic Expression for the Composition of Two Functions Mathematics

If π(π₯) = 3^π₯ and π(π₯) = π₯ β 2, what is (π β π) (π₯)?

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### Video Transcript

If π of π₯ equals three to the power of π₯ and π of π₯ equals π₯ minus two, what is π of π of π₯?

Letβs just begin by recapping this notation, which are read as π of π of π₯. This means that we take an input value π₯, we apply the function π to it, and then we apply the function π to the result. This is called a composite function. Letβs see what that would look like then for these two functions π and π.

We take an input value π₯ and apply the function π. Well, π is the function which subtracts two from its input value. So, π of π₯ is equal to π₯ minus two. Then, we need to apply the function π, by taking this expression for π of π₯ β thatβs π₯ minus two β as the input. So, π of π of π₯ is the same as π of π₯ minus two. Now π of π₯ is the function three to the power of π₯. Itβs three to the power of whatever the input value is. So, π of π₯ minus two is three to the power of π₯ minus two.

So, the composite function π of π of π₯, which is the function obtained when we take an input value, apply the function π, and then apply the function π to the result, is three to the power of π₯ minus two.