Video: Evaluating Cubic Functions

Find the value of 𝑓(8) given the function 𝑓(𝑥) = 𝑥³ − 14.

02:27

Video Transcript

Find the value of 𝑓 eight given the function 𝑓 of 𝑥 equals 𝑥 to the power three, or 𝑥 cubed, minus 14.

In order to work out the value of 𝑓 eight, we need to substitute eight everywhere we see the 𝑥 in the equation. Therefore, 𝑓 of eight equals eight cubed or eight to the power three take away 14. Eight cubed means eight multiplied by eight multiplied by eight again, and not eight multiplied by three. Eight multiplied by eight is 64, and we need to multiply this answer by eight again, 64 multiplied by eight is 512. There are lots of methods of doing this. I will go through a couple at the end for you. In order to get our final answer for the value of 𝑓 eight, we now need to take away 14 from 512 which we know is 498.

Therefore, the answer to the question, find the value of 𝑓 eight where the function 𝑓 of 𝑥 is 𝑥 cubed take away 14, is 498.

If any of you were unsure how to work out 64 multiplied by eight without a calculator, I will now go through a couple of methods for you. One method of working out 64 multiplied by eight is to multiply eight by 60 and then eight by four. 60 multiplied by eight is 480, as six times eight is 48. Four multiplied by eight is 32. We then add these two numbers to give us an answer of 512.

In more traditional methods, we’d start off with multiplying eight by four to give us 32. We carry the three, and then multiply eight by six to give us 48. Add the three that we carried giving us 51. So we have a final answer of 512. There are many other perfectly valid methods for short and long multiplication that you might have been taught in school or seen elsewhere on the internet.

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