9. Find \( (f+g)(x) \) and \( (f-g)(x) \).Then evaluate \( (f+g)(5) \) and \( (f-g)(5) \). \[ f(x)=3 x^{2}+1 \text { and } g(x)=x+4 \]

To find \( (f+g)(x) \) and \( (f-g)(x) \), we simply add and subtract the two functions \( f(x) \) and \( g(x) \): 1. For \( (f+g)(x) \): \[ (f+g)(x) = f(x) + g(x) = (3x^2 + 1) + (x + 4) = 3x^2 + x + 5. \] 2. For \( (f-g)(x) \): \[ (f-g)(x) = f(x) - g(x) = (3x^2 + 1) - (x + 4) = 3x^2 - x - 3. \] Next, we will evaluate \( (f+g)(5) \) and \( (f-g)(5) \): - Evaluating \( (f+g)(5) \): \[ (f+g)(5) = 3(5)^2 + 5 + 5 = 3(25) + 5 + 5 = 75 + 5 + 5 = 85. \] - Evaluating \( (f-g)(5) \): \[ (f-g)(5) = 3(5)^2 - 5 - 3 = 3(25) - 5 - 3 = 75 - 5 - 3 = 67. \] Therefore, we have: \[ (f+g)(x) = 3x^2 + x + 5, \quad (f-g)(x) = 3x^2 - x - 3, \] \[ (f+g)(5) = 85, \quad (f-g)(5) = 67. \]