Problem

Given the functions \( f(x) = 2x - 3 \) and \( g(x) = x^2 - 5 \), find \( (f - g)(x) \)

Answer

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Answer

Step 4: Rearrange the terms to have the highest degree first \( (f - g)(x) = -x^2 + 2x + 2 \)

Steps

Step 1 ：Step 1: Start by setting up the difference of the two functions using the formula \( (f - g)(x) = f(x) - g(x) \)

Step 2 ：Step 2: Substitute the functions into the formula \( (f - g)(x) = (2x - 3) - (x^2 - 5) \)

Step 3 ：Step 3: Simplify the expression \( (f - g)(x) = 2x - 3 - x^2 + 5 \)

Step 4 ：Step 4: Rearrange the terms to have the highest degree first \( (f - g)(x) = -x^2 + 2x + 2 \)

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