Questions: If f(x) = x^2 + 1 and g(x) = 3x + 1, find [f(2) - g(1)]^2

Transcript text: If $f(x)=x^{2}+1$ and $g(x)=3 x+1$, find $[f(2)-g(1)]^{2}$

Solution

To solve the given problem, we need to follow these steps:

Step 1: Evaluate $ f(2) $

Given the function $ f(x) = x^2 + 1 $, we need to find $ f(2) $: \[ f(2) = 2^2 + 1 = 4 + 1 = 5 \]

Step 2: Evaluate $ g(1) $

Given the function $ g(x) = 3x + 1 $, we need to find $ g(1) $: \[ g(1) = 3 \cdot 1 + 1 = 3 + 1 = 4 \]

Step 3: Subtract $ g(1) $ from $ f(2) $

We need to find $ f(2) - g(1) $: \[ f(2) - g(1) = 5 - 4 = 1 \]

Step 4: Square the result

We need to find $ [f(2) - g(1)]^2 $: \[ [f(2) - g(1)]^2 = 1^2 = 1 \]

$\boxed{1}$

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