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Question Video: Finding the Difference between Two Polynomials Functions Mathematics • 9th Grade

Find (𝑓 βˆ’ 𝑔) (π‘₯) given 𝑓(π‘₯) = π‘₯Β² βˆ’ 2 and 𝑔(π‘₯) = π‘₯ βˆ’ 5.

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Video Transcript

Find 𝑓 minus 𝑔 of π‘₯ given 𝑓 of π‘₯ equals π‘₯ squared minus two and 𝑔 of π‘₯ equals π‘₯ minus five.

𝑓 minus 𝑔 of π‘₯ is a combination of functions. In fact, given two functions 𝑓 and 𝑔, 𝑓 minus 𝑔 of π‘₯ is simply 𝑓 of π‘₯ minus 𝑔 of π‘₯. Now, in this case, 𝑓 of π‘₯ is the function π‘₯ squared minus two, whilst 𝑔 of π‘₯ is π‘₯ minus five. So we can say that 𝑓 minus 𝑔 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 we’re subtracting π‘₯ and we’re subtracting negative five. This is the same as subtracting π‘₯ and adding positive five. So we can write 𝑓 minus 𝑔 of π‘₯ as π‘₯ squared minus two minus π‘₯ plus five.

Then, to simplify this expression, we’ll collect like terms. Negative two plus five is positive three. So this simplifies to π‘₯ squared minus π‘₯ plus three. And so given 𝑓 of π‘₯ and 𝑔 of π‘₯ in this case, 𝑓 minus 𝑔 of π‘₯ is π‘₯ squared minus π‘₯ plus three.

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