Decide if the functions in Problems 8–10 are
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- In Problems 12–15, determine whether f is continuous at carrow_forwardIn Problems 11–20, for the given functions f and g. find: (a) (f° g)(4) (b) (g•f)(2) (c) (fof)(1) (d) (g ° g)(0) \ 11. f(x) = 2x; g(x) = 3x² + 1 12. f(x) = 3x + 2; g(x) = 2x² – 1 1 13. f(x) = 4x² – 3; g(x) = 3 14. f(x) = 2x²; g(x) = 1 – 3x² 15. f(x) = Vx; 8(x) = 2x 16. f(x) = Vx + 1; g(x) = 3x %3D 1. 17. f(x) = |x|; g(x) = 18. f(x) = |x – 2|: g(x) x² + 2 2 x + 1 x² + 1 19. f(x) = 3 8(x) = Vĩ 20. f(x) = x³/2; g(x) = X + 1'arrow_forwardCan someone help me with #21?arrow_forward
- 31,37 pleasearrow_forward23. What is the domain of the function f(x) = Vx² – 16? %3D In Problems 25–32, use the given functions f and g. (a) Solve f(x) = 0. (e) Solve g(x) s 0. (b) Solve g(x) = 0. (f) Solve f(x) >g(x).arrow_forwardThe Mean Value Theorem for problem 3 says that between x=-2 and x=2, there exists a value x=c that f'(c) = f(2) -f(-2)/2-(-2). Find the actual value for c which makes the MVT true in this case. Function for problem 3: y=27-x2arrow_forward
- 8. The domain and range of function y= /(5-x)arrow_forward1. Fit the function g(x) = v1x + v2 (x – 1)³ to the data in table below. Xi -1 1 Yi 2 1 -1arrow_forwardLet f(x), g(x) and h(x) be the functions from Problem A.1. Find the derivative of the following function with respect to x: derivative(x) = f(x) . g(x) + f(x) . h(x) - g(x) . h(x)arrow_forward
- 1 2.if (fT))= , find f f(4t)arrow_forwardFor f(x) and g(x) given in Problems 35–38, find (a) (f + g)(x) (b) (f – g)(x) (c) (f'g)(x) (d) (f/g)(x) 35. f(x) = 3x g(x) = x' 36. f(x) = Vx g(x) = 1/x 37. f(x) = V2x g(x) = x² 38. f(x) = (x – 1)? g(x) = 1 – 2x Click to %3D For f(x) and g(x) given in Problems 39–42, find (a) (fº g)(x) (b) (g •f)(x) (c) ƒ(f(x)) (d) f(x) = (f·f)(x) 39. f(x) = (x – 1)³ g(x) = 1 – 2x 40. f(x) = 3x g(x) = x' – 1 41. f(x) = 2Vx g(x) = x* + 5 %3D %3D 1 42. f(x) = g(x) = 4x + 1arrow_forward* The following statement will be used for Problems 2-5 * A UCF mathematics Professor sampled a function f(x) which models a parameter in a physical system. The table below gives the values sampled of f(x) and its derivatives. It is assumed that both f(x) and f'(x) are defined and differentiable for all x. 0. 3. f (x) f'(x) f"(x) 1-1 -3-1-1 0. 0. 4 3 -2 -1 3 Table 1: Sampled values of f(x) and its derivatives Problem 2. Based on Table 1, select the statement that must be true: (A) There exists a point p E (0, 1) such that f (p) = -1. (B))f has at least 4 critical points in (0,5). (C) The equation f(x) - 5 has a solution in [0, 5]. (D) The function f has an inftection point between 4 and 5. (E) There exists a point q E (0,5) such that the slope of the tangent line to the graph of f at (q, f(q)) is 4. 47 니S 2- 4.arrow_forward
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