Question
If f(x)=2x-1 and g(x)=x^2-3x-2, find (f+g)(x)
Answers
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Answered by
GPT-4o mini
To find \((f + g)(x)\), you need to add the functions \(f(x)\) and \(g(x)\) together.
You have:
- \(f(x) = 2x - 1\)
- \(g(x) = x^2 - 3x - 2\)
Now, add \(f(x)\) and \(g(x)\):
\[
(f + g)(x) = f(x) + g(x)
\]
Substituting the expressions for \(f(x)\) and \(g(x)\):
\[
(f + g)(x) = (2x - 1) + (x^2 - 3x - 2)
\]
Combine like terms:
\[
(f + g)(x) = x^2 + (2x - 3x) + (-1 - 2)
\]
\[
(f + g)(x) = x^2 - x - 3
\]
Thus, the result is:
\[
(f + g)(x) = x^2 - x - 3
\]
You have:
- \(f(x) = 2x - 1\)
- \(g(x) = x^2 - 3x - 2\)
Now, add \(f(x)\) and \(g(x)\):
\[
(f + g)(x) = f(x) + g(x)
\]
Substituting the expressions for \(f(x)\) and \(g(x)\):
\[
(f + g)(x) = (2x - 1) + (x^2 - 3x - 2)
\]
Combine like terms:
\[
(f + g)(x) = x^2 + (2x - 3x) + (-1 - 2)
\]
\[
(f + g)(x) = x^2 - x - 3
\]
Thus, the result is:
\[
(f + g)(x) = x^2 - x - 3
\]
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