If f(x)=2x-1 and g(x)=x^2-3x-2, find (f+g)(x)

1 answer

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:

\[ (f + g)(x) = x^2 - x - 3 \]