Questions: Given the following functions, find and simplify (f-g)(x). f(x)=-2 x^2+3 x-2 g(x)=x-4

Given the following functions, find and simplify (f-g)(x). f(x)=-2 x^2+3 x-2 g(x)=x-4
Transcript text: Question Given the following functions, find and simplify $(f-g)(x)$. \[ \begin{array}{l} f(x)=-2 x^{2}+3 x-2 \\ g(x)=x-4 \end{array} \] Do not include " $(f-g)(x)=$ " in your answer. Provide your answer below:
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Solution

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Solution Steps

Step 1: Understand the operation

The problem asks for \((f - g)(x)\), which means we need to subtract the function \(g(x)\) from \(f(x)\).

Step 2: Write down the given functions

\[ f(x) = -2x^2 + 3x - 2 \] \[ g(x) = x - 4 \]

Step 3: Subtract \(g(x)\) from \(f(x)\)

\[ (f - g)(x) = f(x) - g(x) = (-2x^2 + 3x - 2) - (x - 4) \]

Step 4: Distribute the negative sign

\[ (f - g)(x) = -2x^2 + 3x - 2 - x + 4 \]

Step 5: Combine like terms

\[ (f - g)(x) = -2x^2 + (3x - x) + (-2 + 4) \] \[ (f - g)(x) = -2x^2 + 2x + 2 \]

The simplified form of \((f - g)(x)\) is \(-2x^2 + 2x + 2\).

Final Answer

\(\boxed{-2x^2 + 2x + 2}\)

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