Final answer:
To find \((f - g)(x)\), subtract \(g(x)\) from \(f(x)\) and combine like terms, resulting in \(-15x + 59\).
Step-by-step explanation:
The subject of this question is Mathematics, and it is a typical question for a High School level student studying algebra. To find \( (f - g)(x) \) given \( f(x) = 2x + 13 \) and \( g(x) = 17x - 46 \), we subtract the function \( g(x) \) from \( f(x) \):
- Write out the functions: \( f(x) = 2x + 13 \), \( g(x) = 17x - 46 \)
- Subtract function \( g(x) \) from function \( f(x) \): \( (f - g)(x) = f(x) - g(x) \)
- Combine like terms: \( (f - g)(x) = (2x + 13) - (17x - 46) \)
- Simplify the expression: \( (f - g)(x) = 2x + 13 - 17x + 46 \)
- Combine the \( x \) terms and constants: \( (f - g)(x) = -15x + 59 \)
Therefore, the result of \( (f - g)(x) \) is \( -15x + 59 \).