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What is the output when x=-2 |
| Answer» REPLACE the \displaystyle xx in the function with each specified value.Because the input value is a number, 2, we can use algebra to simplify.⎧⎨⎩f(2)=22+3(2)−4=4+6−4=6 In this case, the input value is a letter so we cannot simplify the answer any further.\displaystyle f\left(a\right)={a}^{2}+3a - 4f(a)=a2 +3a−4With an input value of \displaystyle a+ha+h, we must use the distributive property.{f(a+h)=(a+h)2+3(a+h)−4=a2+2ah+h2+3a+3h−4 In this case, we apply the input values to the function more than once, and then perform algebraic operations on the RESULT. We ALREADY found that\displaystyle f\left(a+h\right)={a}^{2}+2ah+{h}^{2}+3a+3h - 4f(a+h)=a2 +2ah+h2 +3a+3h−4and we know that\displaystyle f\left(a\right)={a}^{2}+3a - 4f(a)=a2 +3a−4Now we combine the RESULTS and simplify.⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩⎧⎨⎩f(a+h)−f(a)h=(a2+2ah+h2+3a+3h−4)−(a2+3a−4)h⎧⎪⎪⎪⎨⎪⎪⎪⎩ =2ah+h2+3hh =h(2a+h+3)h{cc{ccFactor out h. =2a+h+3{cc{ccSimplify. | |