Question Video: Evaluating Functions Mathematics

Video Transcript

Find the value of four multiplied by 𝑓 of root three minus four multiplied by 𝑔 of root three given the function 𝑓 of 𝑥 equals 𝑥 squared plus seven 𝑥 and the function 𝑔 of 𝑥 equals seven 𝑥 minus four.

So, the first thing we want to do in this question is to actually work out what our functions are gonna be equal when we substitute in root three for 𝑥 because that’s what it means when it says 𝑓 of root three or 𝑔 of root three. So first of all, we gonna look at 𝑓 of root three. So this is gonna be equal to root three squared because we had 𝑥 squared plus seven multiplied by root three.

So first of all, we’re gonna get three. And that’s because if we remember, root 𝑎 multiplied by root 𝑎 is just equal to 𝑎. So root three multiplied by root three is just equal to three. And reason we get that is cause if we had root three multiplied by root three, you get root nine. Well, root nine is just three. Okay, great, so the second part is going to be add seven root three. And that’s because we had seven multiplied by root three.

Okay, great, so now, we got 𝑓 of root three. Now, let’s get 𝑔 of root three. So now, what we’re gonna have is 𝑔 of root three is equal to seven multiplied by root three minus four, which is gonna be equal to seven root three minus four.

Okay, great, we’ve now got 𝑓 of root three and 𝑔 of root three. So now, we can actually combine them to actually solve the problem cause the problem is asking us to find four multiplied by 𝑓 of root three minus four multiplied by 𝑔 of root three. So therefore, what we’re gonna get is four multiplied by three plus seven root three because that was 𝑓 of root three then minus four multiplied by seven root three minus four because that was 𝑔 of root three.

So now, what we’re gonna do is actually expand the parentheses. So first of all, we have four multiplied by three, which gives us 12. And then, we have four multiplied by seven root three, which gives us positive 28 root three. And then, we have negative four multiplied by seven root three which gives us negative 28 root three. And then, finally, we have negative four multiplied by negative four, which gives us positive 16.

Okay, great, so we now expanded the parentheses, what we need to do is simplify. So first of all, what we have is 12 add 16, which is gonna give us 28. And then, next, what we have is positive 28 root three minus 28 root three. Well, these are actually just gonna cancel each other out. So therefore, we’re just left with 28.

So we can say that the value of four multiplied by 𝑓 of root three minus four multiplied by 𝑔 of root three given the function 𝑓 of 𝑥 equals 𝑥 squared plus seven 𝑥 and the function 𝑔 of 𝑥 equals seven 𝑥 minus four is 28.