For the following problem, (i) graph f and g in the same coordinate system; (ii) solve f(x) = g(x) algebraically to two
decimal places; (iii) solve f(x) > g(x) using parts i and ii; (iv) solve f(x) < g(x) using parts i and ii.
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Question

For the following problem, (i) graph f and g in the same coordinate system; (ii) solve f(x) = g(x) algebraically to two
 decimal places; (iii) solve f(x) > g(x) using parts i and ii; (iv) solve f(x) < g(x) using parts i and ii.
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B) (ii (iii) 0. (

Quizplus · Accepted Answer

(i) Graphing f and g in the same coordinate system: Graph shows that f(x) is always greater than g(x), except at x = 0 where they intersect. (ii) Solving f(x) = g(x) algebraically to two decimal places: f(x) = g(x) x + 1 = 2 / (x - 1) x(x - 1) + 1(x - 1) = 2 x^2 - x + x - 1 = 2 x^2 = 3 x = ±√3 Using a calculator, x ≈ ±1.73 to two decimal places. Therefore, the solutions are x = -1.73 and x = 1.73. (iii) Solving f(x) > g(x) using parts i and ii: From the graph, we can see that f(x) > g(x) for all x except at x = 0. From part (ii), we know that f(x) = g(x) at x = 1.73 and x = -1.73. Therefore, the solution to f(x) > g(x) is x < -1.73 OR x > 0 OR 0 < x < 1.73. (iv) Solving f(x) < g(x) using parts i and ii: From the graph, we can see that f(x) < g(x) only at x = 0. Therefore, the solution to f(x) < g(x) is x = 0.

For the Following Problem, (I) Graph F and G in the Same