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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
- Determine which of the following pairs of functions are linearly independent. 1. f(x) = x² g(x) = 4|x|² NO_ANSWER NO_ANSWER NO_ANSWER NO_ANSWER " ✓ 2. f(x) = e4x ✓ 3. f(0) = cos(30) ✓ 4. f(t) = 3t, g(t) = |t| " g(x) = 4(x-3) 2 g(0) = 4 cos³ (0) - 4 cos(0)arrow_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_forward5. Prove that the functions ex, sin(x), cos(x) = F(R,R) are linearly independent.arrow_forward
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- 4. Examine if functions f(x) f, (x) =x², f;(x)=x² – 2x are linearly = x, independent.arrow_forwardPlease solve question no 97 completelyarrow_forwardDetermine which of the following pairs of functions are linearly independent. ✓ 1. f(x) = 5x g(z) = €5(x-3) ✓2. f(0) = cos(30) g(0) 20 cos¹ (0) - 15 cos(0) 3. f(t) = et cos(ut), g(t)= et sin(ut) ,μ#0 4. f(t) = 3t, g(t) = |t| NO_ANSWER NO_ANSWER NO_ANSWER NO_ANSWER 3arrow_forward
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