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$If $ f(x)=3^{x}+10 $ and $ g(x)=2 x-4 $, find $ (f-g)(x) $. A. $ (f-g)(x)=3^{x}-2 x+14 $ B. $ (f-g)(x)=3^{x}+2 x+6 $ C. $ (f-g)(x)=x+14 $ D. \( (f-g$

If $ f(x)=3^{x}+10 $ and $ g(x)=2 x-4 $, find $ (f-g)(x) $. A. $ (f-g)(x)=3^{x}-2 x+14 $ B. $ (f-g)(x)=3^{x}+2 x+6 $ C. $ (f-g)(x)=x+14 $ D. $ (f-g)(x)=-3^{x}+2 x-14 $

Ask by Ramos Wood.

Feb 05,2025 08:34

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Tutor-Verified Answer

Answer

$ (f - g)(x) = 3^{x} - 2x + 14 $, choice A.

Solution

To find $(f - g)(x)$, subtract $g(x)$ from $f(x)$: \[ \begin{align*} (f - g)(x) &= f(x) - g(x) \\ &= (3^{x} + 10) - (2x - 4) \\ &= 3^{x} + 10 - 2x + 4 \\ &= 3^{x} - 2x + 14 \end{align*} \] **Answer:** A. $ (f-g)(x)=3^{x}-2 x+14 $

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To find $ (f-g)(x) $, we need to subtract the function $ g(x) $ from $ f(x) $: \[ (f-g)(x) = f(x) - g(x) \] Substituting the definitions of $ f(x) $ and $ g(x) $: \[ (f-g)(x) = (3^x + 10) - (2x - 4) \] Now, simplifying this expression: \[ (f-g)(x) = 3^x + 10 - 2x + 4 \] \[ (f-g)(x) = 3^x - 2x + 14 \] So the answer is: A. $ (f-g)(x)=3^{x}-2 x+14 $