Question

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

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