Questions: Question 1 of 10 If f(x)=3x-2 and g(x)=x^2+1, find (f+g)(x). A. 4x^2-1 B. 2x+3 C. x^2+3x-1 D. x^2+3x+1

Question 1 of 10 If f(x)=3x-2 and g(x)=x^2+1, find (f+g)(x). A. 4x^2-1 B. 2x+3 C. x^2+3x-1 D. x^2+3x+1
Transcript text: Question 1 of 10 If $f(x)=3 x-2$ and $g(x)=x^{2}+1$, find $(f+g)(x)$. A. $4 x^{2}-1$ B. $2 x+3$ C. $x^{2}+3 x-1$ D. $x^{2}+3 x+1$
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Solution

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Solution Steps

Step 1: Define the Functions

We are given two functions: \[ f(x) = 3x - 2 \] \[ g(x) = x^2 + 1 \]

Step 2: Compute the Sum of the Functions

To find \((f+g)(x)\), we add the two functions together: \[ (f+g)(x) = f(x) + g(x) = (3x - 2) + (x^2 + 1) \]

Step 3: Simplify the Expression

Now, we simplify the expression: \[ (f+g)(x) = 3x - 2 + x^2 + 1 = x^2 + 3x - 1 \]

Final Answer

The final expression for \((f+g)(x)\) is: \[ \boxed{x^2 + 3x - 1} \]

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