Video: Evaluating Composite Functions at a Given Value

If 𝑓(π‘₯) = 3 βˆ’ π‘₯Β² and 𝑔(π‘₯) = 2π‘₯ + 4, find (𝑓 ∘ 𝑔)(1).

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Video Transcript

If 𝑓 of π‘₯ equals three minus π‘₯ squared and 𝑔 of π‘₯ equals two π‘₯ plus four, find 𝑓 of 𝑔 of one.

What we’re doing is we’re completing the composition of functions. So we can rewrite this in a way that might make a little more sense. It can be written as 𝑓 of 𝑔 of one. It’s said the same way, but written a little bit differently. So essentially, we plug one into the 𝑔 function, and then whatever we get for that, we will take that number and plug it into the 𝑓 function.

So first, let’s plug one into the 𝑔 function for π‘₯. So instead of two π‘₯ plus four, it’s two times one plus four; we’re plugging in one. And two times one is two plus four is six. So now we’re gonna plug six into the 𝑓 of π‘₯ function, so we have three minus six squared, and three minus 36 is equal to negative 33.

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