Solve the following operations. Given: f(x)=2x+3 g(x)= 3x-2 h(x)6x2+5x-6 1. (f+g) (x) 2. (f+g) (-2) 3. (f-g) (x) 4. (f-g) (3) 5. (f.g) (x) 6. (f.g) (-2) 7. f/h(x) 8. f/h (-1)
Answer (1)
Answer:Given functions: - f(x) = 2x + 3- g(x) = 3x - 2- h(x) = 6x^2 + 5x - 6 1. (f + g)(x) = f(x) + g(x) = (2x + 3) + (3x - 2) = 5x + 12. (f + g)(-2) = f(-2) + g(-2) = (2(-2) + 3) + (3(-2) - 2) = (-4 + 3) + (-6 - 2) = -1 - 8 = -93. (f - g)(x) = f(x) - g(x) = (2x + 3) - (3x - 2) = -x + 54. (f - g)(3) = f(3) - g(3) = (2(3) + 3) - (3(3) - 2) = (6 + 3) - (9 - 2) = 9 - 7 = 25. (f * g)(x) = f(x) * g(x) = (2x + 3)(3x - 2) = 6x^2 - 4x + 9x - 6 = 6x^2 + 5x - 66. (f * g)(-2) = f(-2) * g(-2) = (2(-2) + 3)(3(-2) - 2) = (-4 + 3)(-6 - 2) = -1 * -8 = 87. f/h(x) = f(x)/h(x) = (2x + 3)/(6x^2 + 5x - 6)8. f/h(-1) = f(-1)/h(-1) = (2(-1) + 3)/(6(-1)^2 + 5(-1) - 6) = (2 + 3)/(6 - 5 - 6) = 5/-5 = -1 Please note that for division (f/h), we need to keep the expression as is since it involves a quadratic function in the denominator. Let me know if you need further assistance with the division or any other calculations.
