20. A linear function is shown.f(x) = (-5/2)x - 3A. Create a linear function g(x) such that f(x) = g(x) has exactly one solution.B. What is the exact solution to f(x) = g(x)?Answer A:Answer B:
Accepted Solution
A:
Answer:g(x) = (1/2)x + 3f(x) = g(x) at (-1/2 , 13/4)Step-by-step explanation:g(x) and f(x) will have exactly one solution when they are not parallel (same slope) and when they are not equivalent functions (like doubling or halving all terms).f(x) = (-5/2)x - 3g(x) = (1/2)x + 3 <= choose an easy equation.To find the solution, equate the two functions:f(x) = g(x)(-5/2)x - 3 = (1/2)x + 3(-5/2)x - (1/2)x = 3 + 3 <= move variables to one side, constants to other(-6/2)x = 6 <= simplifyx = 6 / (-6/2) <=isolate xx = -6/12x = -1/2Substitute x = -1/2 into any equation to find yg(x) = (1/2)x + 3g(1/2) = (1/2)(1/2) + 3g(1/2) = (1/4) + 3g(1/2) = (1/4) + (12/4) <= find common denominator to addy = (13/4) <= the function symbol can be replaced by yThe coordinates are (-1/2 , 13/4).