For the given functions f and g , complete parts (a)-(h). F parts (a)-(d), also find the domain. \[ f(x)=5 x+2 ; g(x)=7 x-8 \] \( (f+g)(x)=12 x-6 \) (Simplify-your answer. \( ) \) What is the domain of \( f+g \) ? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The domain is \( \{x \mid\} \). (Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) The domain is \( \{x \mid x \) is any real number \( \} \). (b) Find \( (f-g)(x) \). \( (f-g)(x)= \) \( \square \) (Simplify your answer.)

Let's solve the problem step by step. ### Given Functions We have the following functions: \[ f(x) = 5x + 2 \] \[ g(x) = 7x - 8 \] ### Part (a): Find \( (f+g)(x) \) To find \( (f+g)(x) \), we add the two functions together: \[ (f+g)(x) = f(x) + g(x) = (5x + 2) + (7x - 8) \] Now, let's simplify this expression: \[ (f+g)(x) = 5x + 2 + 7x - 8 = (5x + 7x) + (2 - 8) = 12x - 6 \] So, we have: \[ (f+g)(x) = 12x - 6 \] ### Domain of \( f+g \) The domain of \( f(x) \) and \( g(x) \) is all real numbers since they are both linear functions. Therefore, the domain of \( f+g \) is also all real numbers. The domain is: \[ \{x \mid x \text{ is any real number} \} \] ### Part (b): Find \( (f-g)(x) \) To find \( (f-g)(x) \), we subtract \( g(x) \) from \( f(x) \): \[ (f-g)(x) = f(x) - g(x) = (5x + 2) - (7x - 8) \] Now, let's simplify this expression: \[ (f-g)(x) = 5x + 2 - 7x + 8 = (5x - 7x) + (2 + 8) = -2x + 10 \] So, we have: \[ (f-g)(x) = -2x + 10 \] ### Summary of Results - \( (f+g)(x) = 12x - 6 \) - Domain of \( f+g \): \( \{x \mid x \text{ is any real number} \} \) - \( (f-g)(x) = -2x + 10 \) If you need further parts (c)-(h) or any additional information, please let me know!