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Determine Ihe x-values at which Ihe graphs of { and g cross. If no such x-values exist, state that factI(x) = 169, g(x) =x2 Seleci the correct cholce below and; It ...

Question

Determine Ihe x-values at which Ihe graphs of { and g cross. If no such x-values exist, state that factI(x) = 169, g(x) =x2 Seleci the correct cholce below and; It necessary; Iill In Ihe answer box t0 complete your choice (Use comma t0 separate answers as needed ) There are no such x-values

Determine Ihe x-values at which Ihe graphs of { and g cross. If no such x-values exist, state that fact I(x) = 169, g(x) =x2 Seleci the correct cholce below and; It necessary; Iill In Ihe answer box t0 complete your choice (Use comma t0 separate answers as needed ) There are no such x-values



Answers

Determine the $x$ -values at which the graphs of f and $g$ cross. If no such $x$ -values exist, state that fact. $$f(x)=9, \quad g(x)=x^{2}$$

In problem 13. We want to get all X values at which f of X and G of X intersect If you have tow functions. Ah, we're here x and y, for example, we have function every few weeks and another function G of X. If they intersect at one point like this at X one, they must have the same value off. Why? Why you want meaning that toe get all X values at which F and G crosse we equip it f of x and G of X and solve this equation. We have Year seven equals X squared minus three x plus two. We subtract both sides from seven. We have year zero equals X squared minus three X minus five plus two minus seven equals minus five. Using factory ization, you want to get a number two numbers that when we multiply them gives us minus five and when we add them gives us minus three. The multiplication off five is one. The factors of five is one on five. If you want to use fertilization, it will be very hard. Then we can use the general lute off the second degree problem like this where the value off X equals minus B plus or minus square. Root off B squared minus four. Easy Divided by two A. Where a B and C is the factors off X squared X and extra bottle off. Zero equals X squared plus PX plus C. This means a equals one b equals minus three C equals minus five. Then X equals minus minus. B is three plus or minus square. Root off B squared is dying minus four. Multiplied by a not to blow it by sea. Divided by two e equals three plus or minus square. Root off nine plus 20 is 29 divided by two. And this is the values off X. Where is she? And if intersect and the final answer off our problems, we have here to values first. The value three plus square root of 29 by two and second value is three minus square root of 29 divided by two

In problem 14. We want to get all X values where f and G intersects if they intersects eggs and boy and we have here. If this is the function f of X and this the function g of X for example, if they intersect at the point, for example X one, they must have the same value of oy. Why you want, for example, meaning that toe get all X values at which F and G crosse we equate the two functions f of X equals e g of X, then the solution off this equation is the X values we need. Let's substitute by the expression off each of H function we have minus six equals X squared plus three x plus 13 We add sexto both sides. We have Year zero equals X squared lost three x plus by 19. It's hard toe make factory ization for this problem. Then we can use the general rule toe get the solution off this equation. The general form off this equation, it equals x squared plus p x plus c. This means we have a equals one b equals three and C equals 19 and the general rule X equals minus B plus or minus square. Root off P. Squared minus four a. C. Divided by two A. Let's substitute by the values of A, B and C Get the solution off X. It equals minus three plus or minus square root of nine three squared minus four multiplied by a multiplied by. See she's 19 divided by to multiply it by. We can notice that this term under the square root is a negative, has a negative sign, which means there is no intersect, and this is has no solution. In the real numbers. X has no solution because this is square off a negative number, meaning that f of x n g off X they never intersect, never intersect or never cross on. This is the final answer off our problems.

In problem 12. We want to get all values of X at which, if n g intersects, if you have two functions for example f of X and other functions Gox We want to get the points at which they intersect. For example, if they intercept at X one here, they must have the same value off. Why here? If these X axis and this vortex this is why one meaning that to get old the intersection between F and G or all X values where F and G crosse we equate f of x and Geo Vicks or eight equals half x squared. We multiply both sides by two. We get 16 equals X squared. We subtract 16 from both sides we get zero equals X squared minus 16. Using factory ization, we get zero equals X minus four multiplied by X plus four. This means we have the first solution when X minus four equals zero or X one equals four. The second solution comes from this bracket Toby zero X plus four equals zero. The second solution X two equals minus four and this is the values were f of X and G of X intersect and the final answer off our problems

In problems. Christine, we want toe get all X values at which f of X and G off x intersects. If we have here the function f of X for example, dysfunction and the function g a voi dysfunction. For example, If the Intersect at the point for example this point they must have x one and why one the same. They must have the same value for both functions. This means if you want to get the X values at which f of X and G of X intersect, we equip it f of X and G of X, where the solution off this equation is the answer we need. It's substitute by the explorations off each function we have here X equals X squared minus seven, X plus 20 and G of X equals two x plus six. We subtract minus two x from both sides. We have X squared minus nine X plus 20 equal six. We subtract six from both sides. X squared minus nine X plus 14 equals zero. Let's find two numbers that have the multiplication off 14 and the submission off. Nine off minus nine. The multiplication is 14 and the submission off minus nine. The multiplication is for 14 is one multiplied by 14 or two multiplied by seven or minus two. Multiply by minus seven, and we have to get to numbers that have. There's some equals. Minus nine. We have two and seven. If we added minus two and minus seven, there's some is minus nine and we have minus two and minus seven. Their multiplication is 14. This means the factory ization off. This equation is x close, X minus two X months to and X minus seven equals zero. From the first bracket, we get X equals two X one equals two from the first factor. And from the second factor, we have X two equals seven and these or the values of X at which f of X and G off intersect. And this is the final answer off our problem.


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