Video Transcript
Find π minus π of π₯ given π of π₯ equals π₯ squared minus two and π of π₯ equals π₯ minus five.
π minus π of π₯ is a combination of functions. In fact, given two functions π and π, π minus π of π₯ is simply π of π₯ minus π of π₯. Now, in this case, π of π₯ is the function π₯ squared minus two, whilst π of π₯ is π₯ minus five. So we can say that π minus π of π₯ must simply be π₯ squared minus two minus π₯ minus five. Now, of course, we do need to be really careful here when subtracting π₯ minus five. This is the same as subtracting each part of the expression inside our parentheses. So weβre subtracting π₯ and weβre subtracting negative five. This is the same as subtracting π₯ and adding positive five. So we can write π minus π of π₯ as π₯ squared minus two minus π₯ plus five.
Then, to simplify this expression, weβll collect like terms. Negative two plus five is positive three. So this simplifies to π₯ squared minus π₯ plus three. And so given π of π₯ and π of π₯ in this case, π minus π of π₯ is π₯ squared minus π₯ plus three.
