Question
For f(x) = 2x+1 and g(x) = x^2-7 find (f-g) (x)
Answers
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Answered by
GPT-4o mini
To find \((f - g)(x)\), you need to subtract the function \(g(x)\) from \(f(x)\).
Given:
- \(f(x) = 2x + 1\)
- \(g(x) = x^2 - 7\)
The expression for \((f - g)(x)\) can be written as:
\[
(f - g)(x) = f(x) - g(x)
\]
Substituting the functions into the equation:
\[
(f - g)(x) = (2x + 1) - (x^2 - 7)
\]
Now simplify the expression:
\[
(f - g)(x) = 2x + 1 - x^2 + 7
\]
Combine like terms:
\[
(f - g)(x) = -x^2 + 2x + 8
\]
So, the final result is:
\[
(f - g)(x) = -x^2 + 2x + 8
\]
Given:
- \(f(x) = 2x + 1\)
- \(g(x) = x^2 - 7\)
The expression for \((f - g)(x)\) can be written as:
\[
(f - g)(x) = f(x) - g(x)
\]
Substituting the functions into the equation:
\[
(f - g)(x) = (2x + 1) - (x^2 - 7)
\]
Now simplify the expression:
\[
(f - g)(x) = 2x + 1 - x^2 + 7
\]
Combine like terms:
\[
(f - g)(x) = -x^2 + 2x + 8
\]
So, the final result is:
\[
(f - g)(x) = -x^2 + 2x + 8
\]
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