Answer :
To solve for \( (f - g)(x) \) given the functions \( f(x) = x + 8 \) and \( g(x) = -4x - 3 \), follow these steps:
1. Express \( (f - g)(x) \) in terms of \( f(x) \) and \( g(x) \):
[tex]\[ (f - g)(x) = f(x) - g(x) \][/tex]
2. Substitute the given functions \( f(x) \) and \( g(x) \) into the expression:
[tex]\[ (f - g)(x) = (x + 8) - (-4x - 3) \][/tex]
3. Simplify the expression by distributing the negative sign and combining like terms:
[tex]\[ (f - g)(x) = x + 8 + 4x + 3 \][/tex]
4. Combine the \( x \) terms and the constant terms:
[tex]\[ (f - g)(x) = (x + 4x) + (8 + 3) \][/tex]
[tex]\[ (f - g)(x) = 5x + 11 \][/tex]
So, the function \( (f - g)(x) \) is:
[tex]\[ (f - g)(x) = 5x + 11 \][/tex]
1. Express \( (f - g)(x) \) in terms of \( f(x) \) and \( g(x) \):
[tex]\[ (f - g)(x) = f(x) - g(x) \][/tex]
2. Substitute the given functions \( f(x) \) and \( g(x) \) into the expression:
[tex]\[ (f - g)(x) = (x + 8) - (-4x - 3) \][/tex]
3. Simplify the expression by distributing the negative sign and combining like terms:
[tex]\[ (f - g)(x) = x + 8 + 4x + 3 \][/tex]
4. Combine the \( x \) terms and the constant terms:
[tex]\[ (f - g)(x) = (x + 4x) + (8 + 3) \][/tex]
[tex]\[ (f - g)(x) = 5x + 11 \][/tex]
So, the function \( (f - g)(x) \) is:
[tex]\[ (f - g)(x) = 5x + 11 \][/tex]
