To find \((f - g)(x)\), we need to subtract \(g(x)\) from \(f(x)\).
Given:
- \(f(x) = 2^x - 3x\)
- \(g(x) = 1 - 2x\)
Now, we can perform the subtraction:
\[ (f - g)(x) = f(x) - g(x) \]
Substituting in the functions:
\[ (f - g)(x) = (2^x - 3x) - (1 - 2x) \]
Distributing the negative sign to \(g(x)\):
\[ (f - g)(x) = 2^x - 3x - 1 + 2x \]
Now, combine like terms:
\[ (f - g)(x) = 2^x - (3x - 2x) - 1 \] \[ (f - g)(x) = 2^x - x - 1 \]
Thus, the final answer is:
\[ (f - g)(x) = 2^x - x - 1 \]