Questions: Find (f+g)(x) if f(x)=4x^2-5x and g(x)=3x^2+6x-4.

Find (f+g)(x) if f(x)=4x^2-5x and g(x)=3x^2+6x-4.
Transcript text: Find $(f+g)(x)$ if $f(x)=4 x^{2}-5 x$ and $g(x)=3 x^{2}+6 x-4$.
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Solution

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Solution Steps

Step 1: Identify the Functions

We are given two functions: \[ f(x) = 4x^2 - 5x \] \[ g(x) = 3x^2 + 6x - 4 \]

Step 2: Add the Functions

To find \((f+g)(x)\), we add the two functions: \[ (f+g)(x) = f(x) + g(x) = (4x^2 - 5x) + (3x^2 + 6x - 4) \]

Step 3: Combine Like Terms

Combine the like terms:

  • Combine the \(x^2\) terms: \(4x^2 + 3x^2 = 7x^2\)
  • Combine the \(x\) terms: \(-5x + 6x = x\)
  • The constant term is \(-4\)

Thus, \((f+g)(x) = 7x^2 + x - 4\).

Final Answer

The correct expression for \((f+g)(x)\) is: \[ \boxed{(f+g)(x) = 7x^2 + x - 4} \]

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