About this video
This short video works through a function table to find the x-value where F of x minus G of x equals x. The instructor tests each candidate x-value by substituting the table values, rules out the ones that fail, and confirms that x equals 3 is the answer. A final check at x equals 4 shows why it does not work there.
You'll be able to
- read values of F(x) and G(x) from a table and subtract them correctly.
- test candidate x-values against the condition F(x) - G(x) = x.
- confirm a solution by substituting it back and checking the result.
Key words
- Function
- A rule that gives exactly one output value for each input x.
- Substitution
- Replacing a variable with a specific value to evaluate an expression.
- Subtracting a negative
- Subtracting a negative number is the same as adding its positive, so a minus negative nine equals plus nine.
- Verification
- Checking a candidate answer by plugging it back into the original condition.
Transcript
- [Instructor] We're told the table above shows some values of the functions F and G. For which value of X is F of X minus G of X equal to X? Pause this video and see if you can figure this out. All right, so they give a bunch of X values and for each of those X values we see, for example, when X equals zero what F of zero is and we see what G of zero is.
Now we need to figure out when F of X minus G of X is equal to X, or another way to think about it, when the number here minus the number here is equal to the number right over there. So let's just try them out. What's nine minus negative nine? Well, that would be positive 18, not zero.
So we can rule that one out. What's eight minus negative seven? Well, that would be positive 15, not one. We can rule that out. What's five minus negative five? Well, that would be positive 10, not two. Rule that out. What is zero minus negative three? Well, that's going to be positive three, which is what X was right over here.
So that's the answer. That's the value of X for which F of X minus G of X is equal to X. It's three. We can verify for four. Let's see, F of four is negative seven. So negative seven minus negative one is going to be negative seven plus one, which is negative six, not four.
So yeah, we like that choice.
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