Supposed f(x) = 2" - 3x and g(x) = 1 - 2x.

Question

What is (f - g)(x)?
Hint - Subtract f(x) and g(x), distribute the negative sign to g(x), and combine like terms.
Answer: choose your answer...

Answer 1

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:

\[ (f - g)(x) = 2^x - x - 1 \]