\( f(x)=7 x^{2}+7 x-2, g(x)=6 x-7 \) find \( (f+g)(-6) \) Your Answer:

1. Write down the definitions of \( f(x) \) and \( g(x) \): - \( f(x) = 7x^2 + 7x - 2 \) - \( g(x) = 6x - 7 \) 2. Find the sum \( (f+g)(x) \) by adding \( f(x) \) and \( g(x) \) together: \[ (f+g)(x) = f(x) + g(x) = (7x^2 + 7x - 2) + (6x - 7) \] 3. Combine like terms: - The \( x^2 \) term: \( 7x^2 \) - The \( x \) terms: \( 7x + 6x = 13x \) - The constant terms: \( -2 - 7 = -9 \) \[ (f+g)(x) = 7x^2 + 13x - 9 \] 4. Substitute \( x = -6 \) into \( (f+g)(x) \): \[ (f+g)(-6) = 7(-6)^2 + 13(-6) - 9 \] 5. Evaluate step by step: - Calculate \((-6)^2\): \[ (-6)^2 = 36 \] - Multiply by 7: \[ 7 \times 36 = 252 \] - Multiply 13 by \(-6\): \[ 13 \times (-6) = -78 \] - Now sum the results: \[ (f+g)(-6) = 252 - 78 - 9 \] 6. Final computation: \[ 252 - 78 = 174 \] \[ 174 - 9 = 165 \] Therefore, the final answer is: \[ \boxed{165} \]