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

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 $[f(2)-g(1)]^{2}$
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Solution

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Solution Steps

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

  1. Evaluate \( f(2) \) using the function \( f(x) = x^2 + 1 \).
  2. Evaluate \( g(1) \) using the function \( g(x) = 3x + 1 \).
  3. Subtract \( g(1) \) from \( f(2) \).
  4. Square the result of the subtraction.
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 \( [f(2) - g(1)]^2 \): \[ [f(2) - g(1)]^2 = 1^2 = 1 \]

Final Answer

\(\boxed{1}\)

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