Question
Let \( f(x)=x^{2}+4 \) and \( g(x)=2 x-4 \) Find \( (f-g)(x) \)
Ask by Chang Conner. in the United States
Dec 03,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( (f-g)(x) = x^{2}+8-2x \)
Solution
Calculate or simplify the expression \( x^{2}+4-2x+4 \).
Simplify the expression by following steps:
- step0: Solution:
\(x^{2}+4-2x+4\)
- step1: Add the numbers:
\(x^{2}+8-2x\)
The expression \( (f-g)(x) \) simplifies to \( x^{2}+8-2x \).
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Beyond the Answer
To find \( (f - g)(x) \), we need to subtract the function \( g(x) \) from the function \( f(x) \). We have: \[ f(x) = x^2 + 4 \] \[ g(x) = 2x - 4 \] Now, we can compute \( (f - g)(x) \): \[ (f - g)(x) = f(x) - g(x) = (x^2 + 4) - (2x - 4) \] Distributing the negative sign gives us: \[ f(x) - g(x) = x^2 + 4 - 2x + 4 \] Combining like terms, we have: \[ f(x) - g(x) = x^2 - 2x + 8 \] Thus, \( (f - g)(x) = x^2 - 2x + 8 \).
