Video: US-SAT04S3-Q04-832171082847

If 𝑓(π‘₯) = 5 + 3π‘₯, which of the following is equivalent to 𝑓(βˆ’3π‘₯)? [A] 5 βˆ’ 9π‘₯Β² [B] 5 βˆ’ 3π‘₯ [C] 5 βˆ’ 9π‘₯ [D] 5 + 3π‘₯Β²

01:20

Video Transcript

If 𝑓 of π‘₯ equals five plus three π‘₯, which of the following is equivalent to 𝑓 of negative three π‘₯?

We’re starting out with 𝑓 of π‘₯ equals five plus three π‘₯. And we need to plug in negative three π‘₯ for the π‘₯-value. This means that anywhere in our function where π‘₯ shows up we need to replace it with negative three π‘₯. After we do that, we can simplify the second function, bring down the five. We can multiply three by negative three, which gives negative nine and that’s been multiplied by π‘₯.

We could also think of it another way. We could think of it as multiplying the π‘₯ that’s there by negative three. And in that case, every place we see π‘₯, we would need to multiply that π‘₯ by negative three. The expression would then be three times negative three times π‘₯. And that simplifies to negative nine π‘₯.

The only answer choice that reflects this expression is c five minus nine π‘₯.

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