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

1 answer

To find \((f+g)(x)\), we need to add the functions \(f(x)\) and \(g(x)\) together.

Given:

  • \(f(x) = 2x + 1\)
  • \(g(x) = x^2 - 7\)

We can calculate \((f+g)(x)\) as follows:

\[ (f+g)(x) = f(x) + g(x) = (2x + 1) + (x^2 - 7) \]

Now, we combine the terms:

\[ (f+g)(x) = 2x + 1 + x^2 - 7 \]

\[ (f+g)(x) = x^2 + 2x + (1 - 7) \]

\[ (f+g)(x) = x^2 + 2x - 6 \]

Thus, the result is:

\[ (f+g)(x) = x^2 + 2x - 6 \]