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\begin{tabular}{l}\( f(x)=5 x+2 \) and \( g(x)=2 x+8 \) \\ Find \( g[f(-4)] \) \\ -28 \\ \hline 18 \\ \hline 16 \\ \( 0-16 \)\end{tabular}

Ask by Rodriguez Murphy. in the Philippines
Dec 07,2024

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\( g[f(-4)] = -28 \)

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The Deep Dive

To find \( g[f(-4)] \), we’ll first calculate \( f(-4) \). 1. Substitute \( -4 \) into \( f(x) \): \[ f(-4) = 5(-4) + 2 = -20 + 2 = -18 \] Now, we will use this result to find \( g[f(-4)] \) or \( g(-18) \): 2. Substitute \( -18 \) into \( g(x) \): \[ g(-18) = 2(-18) + 8 = -36 + 8 = -28 \] So the final answer is \(-28\). --- Learning about linear functions can be quite fascinating! They can model many real-world situations, like predicting profits, population growth, and even certain physical phenomena. Understanding how to navigate functions like \( f(x) \) and \( g(x) \) allows you to visualize relationships and make informed predictions. If you find yourself working with composite functions like \( g[f(x)] \) often, make sure to keep your notations clear! Common mistakes include mixing up the order of operations and misplacing negative signs. Always double-check your calculations to avoid slight slips that can lead to entirely different outcomes.

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