Questions: For the given functions f and g, complete parts (a)-(h). For parts (a)-(d), also find the domain, f(x) = x - 3; g(x) = 5x^2 (a) Find (f+g)(x). (f+g)(x) = (Simplify your answer. Do not factor.)

For the given functions f and g, complete parts (a)-(h). For parts (a)-(d), also find the domain, f(x) = x - 3; g(x) = 5x^2 (a) Find (f+g)(x). (f+g)(x) = (Simplify your answer. Do not factor.)
Transcript text: For the given functions $\mathbf{f}$ and g , complete parts (a)-(h). For parts (a)-(d), also find the domain, \[ f(x)=x-3 ; g(x)=5 x^{2} \] (a) Find $(f+g)(x)$. \[ (f+g)(x)= \] $\square$ (Simplify your answer. Do not factor.) Clear all Check ans Ask my instructor Share Download
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Solution

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Solution Steps

Step 1: Identify the given functions

The given functions are: \[ f(x) = x - 3 \quad \text{and} \quad g(x) = 5x^2. \]

Step 2: Understand the operation to perform

We are asked to find \((f + g)(x)\), which is the sum of the functions \(f(x)\) and \(g(x)\).

Step 3: Add the functions

Add \(f(x)\) and \(g(x)\) together: \[ (f + g)(x) = f(x) + g(x) = (x - 3) + 5x^2. \]

Step 4: Simplify the expression

Combine like terms: \[ (f + g)(x) = 5x^2 + x - 3. \]

Final Answer

\((f + g)(x) = 5x^2 + x - 3\)

\(\boxed{5x^2 + x - 3}\)

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