Given the functions:
$$
f(x)=2 x \quad g(x)=|x-4| \quad h(x)=\frac{1}{x+5}
$$

Evaluate the function $(f-g)(x)$ for $x=6$. $(f-g)(6)$ is $\square$. $\square$

Question

Given the functions:
$$
f(x)=2 x \quad g(x)=|x-4| \quad h(x)=\frac{1}{x+5}
$$

Evaluate the function $(f-g)(x)$ for $x=6$. $(f-g)(6)$ is $\square$. $\square$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Given the functions: $f(x) = 2x$, $g(x) = |x - 4|$, and $h(x) = \frac{1}{x+5}$, we need to evaluate $(f - g)(x)$ for $x = 6$. ‖ ‖ step 2 ⋮ Calculate $f(6)$: $f(6) = 2 \cdot 6 = 12$. ‖ ‖ step 3 ⋮ Calculate $g(6)$: $g(6) = |6 - 4| = |2| = 2$. ‖ ‖ step 4 ⋮ Subtract $g(6)$ from $f(6)$: $(f - g)(6) = f(6) - g(6) = 12 - 2 = 10$. ‖ ∻Answer∻ ⚹ $(f - g)(6) = 10$ ⚹ ∻Key Concept∻ ⚹Function Evaluation⚹ ∻Explanation∻ ⚹To evaluate $(f - g)(x)$ for a given $x$, calculate $f(x)$ and $g(x)$ separately, then subtract $g(x)$ from $f(x)$.⚹◊What is the difference between two functions, $(f - g)(x)$, when $x = 6$ based on the provided functions $f(x)$ and $g(x)$?⍭ Generate me a similar question◊

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