Questions: f(x)=x^2+4 x-2, g(x)=x+8, Find (f-g)(x)

f(x)=x^2+4 x-2, g(x)=x+8, Find (f-g)(x)
Transcript text: $\begin{array}{l}f(x)=x^{2}+4 x-2 \\ g(x)=x+8 \\ \text { Find }(f-g)(x)\end{array}$
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Solution

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Solution Steps

Step 1: Define the Functions

We have two functions defined as follows: \[ f(x) = x^2 + 4x - 2 \] \[ g(x) = x + 8 \]

Step 2: Calculate \( (f-g)(x) \)

To find \( (f-g)(x) \), we subtract \( g(x) \) from \( f(x) \): \[ (f-g)(x) = f(x) - g(x) = (x^2 + 4x - 2) - (x + 8) \] Simplifying this expression: \[ (f-g)(x) = x^2 + 4x - 2 - x - 8 = x^2 + 3x - 10 \]

Step 3: Evaluate \( (f-g)(5) \)

Now, we evaluate \( (f-g)(x) \) at \( x = 5 \): \[ (f-g)(5) = 5^2 + 3(5) - 10 \] Calculating this step-by-step: \[ = 25 + 15 - 10 = 30 \]

Final Answer

The value of \( (f-g)(5) \) is \[ \boxed{30} \]

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