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In Problems 27–32, use Definition 1 to determine whether the functions
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Fundamentals of Differential Equations and Boundary Value Problems
- In 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_forward(15) Determine whether or not the functions y₁ 4x³, y2 = π, y3 = 12x², and y4 = 24x are linearly independent on any interval. Show all work to support your answer.arrow_forward2. Let P(t) represent the population of Los Angeles t years after 1900. (a) Interpret P(10) = 319, 198 in words. P(10) - Р(0) (b) Given that P(0) = 102, 479 and P(10) = 319, 198, calculate and interpret 10 – 0 in words. (c) of Los Angeles reached 200,000. Set up an equation that could be used to find how many years after 1900 the populationarrow_forward
- The functions f₁(x)=e(x+a), f2(x)=e(x+b), and f3(x)=e(x+c), where a, b, and care constants, are LINEARLY INDEPENDENT. O True Falsearrow_forwardSuppose m and b are constants. What is the linearization of the function f(x) = mx + b at any given point x = a ?arrow_forward1. Find the linearization of x3 − x at a = 2.arrow_forward
- Under what circumstances is a linear function f(x) = mx + b odd? Can a linear function ever be even?arrow_forward2) For over 20 years, the population of Tressel, Ohio has been increasing linearly according tothe function P(t) = 225t + 7,000 where P is the number of residents, and t is years after 1980. Compute P(0) and interpret its meaning in the context of this problem.arrow_forwardIn Problems 49–56, for each graph of a function y = f(x), find the absolute maximum and the absolute minimum, if they exist. Identify any local maximum values or local minimum values.arrow_forward
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