For f(x) = 2x+1 and g(x) = x^2-7 find (f-g) (x)

1 answer

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:

\[ (f - g)(x) = -x^2 + 2x + 8 \]