# Video: US-SAT04S3-Q04-832171082847

If 𝑓(𝑥) = 5 + 3𝑥, which of the following is equivalent to 𝑓(−3𝑥)? [A] 5 − 9𝑥² [B] 5 − 3𝑥 [C] 5 − 9𝑥 [D] 5 + 3𝑥²

01:20

### Video Transcript

If 𝑓 of 𝑥 equals five plus three 𝑥, which of the following is equivalent to 𝑓 of negative three 𝑥?

We’re starting out with 𝑓 of 𝑥 equals five plus three 𝑥. And we need to plug in negative three 𝑥 for the 𝑥-value. This means that anywhere in our function where 𝑥 shows up we need to replace it with negative three 𝑥. 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 𝑥.

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

The only answer choice that reflects this expression is c five minus nine 𝑥.