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Question: 8 following is a statement of a theorem about certain...

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8. Following is a statement of a theorem about certain cubic equations. For this theorem, b represents a real number. Theorem A. If f is a cubic function of the form f(x) = x3-x + b and b>1, then the function f has exactly one x-intercept. Following is another theorem about x-intercepts of functions: Theorem B. If f and g are functions with gx)k.f(x), where k is a nonzero real number, then f and g have exactly the same x-intercepts. Using only these two theorems and some simple algebraic manipulations, what can be concluded about the functions given by the following formulas? (a) f(x) x3-x + 7 (b) g(x) x3 +x 7 (e) h(x)-x3 + x -5 (d) k(x) 2x32x +3 (e) r(x)x4-x +11 (D F(x) 2x3 -2x +7
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