Going to evaluate F of, actually let's just start What it means to evaluate F of, not X, but we're What do I mean by that? Well, let's think about Up a function by composing one function of other functions or I guess you could think of nesting them. To compose functions? Well that means to build This video is introduce you to the idea of composing functions. And actually let me number this one, two, three, just like that. So for example, when X is equal to three, H of X is equal to zero. So you could use this asĪ definition of G of T. We map between different values of T and what G of T would be. Voiceover:So we have three different function definitions here. The quadratic formula yields roots 3 ± √5. We can continue to search for roots by finding the roots of the quadratic: From our analysis above, we know that (x - 1) is a factor of the polynomial, so we want to divide the polynomial by (x - 1) and find the quotient. Here is the systematic algebraic way to do it: Your second question asks if there is an easier way to solve the following equation: Therefore (x - 1) is indeed a factor of 2x³ - 14x² + 20x - 8. Which we note is 0, because the first 3 terms are from the original function ƒ(x) and that already yielded 8, and when we combine that with the remaining -8, we get 0. If we divide by (x - 1) our remainder is: Since the remainder is 8 and we want to get rid of that, we subtract 8 to get: We can make (x - 1) a factor of ƒ(x) if we add something to the function that will get rid of the remainder. It follows that if we divide ƒ(x) by (x - 1), then our remainder is 8. Remainder Theorem tells us that when we divide ƒ(x) by a linear binomial of the form (x - a) then the remainder is ƒ(a). That means when you plug in 1 for "x" in the above expression, you will get 8.
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