Questions: Let f(x)=2x+3 and g(x)=x^2-1 B. Find (f+g)(x).

Transcript text: Let $f(x)=2 x+3$ and $g(x)=x^{2}-1$ B. Find $(\mathrm{f}+\mathrm{g})(\mathrm{x})$.

Solution

To find $(f+g)(x)$, we need to add the functions $f(x)$ and $g(x)$. This involves adding the expressions for $f(x)$ and $g(x)$ together.

Step 1: Define the Functions

We are given two functions: $ f(x) = 2x + 3 $ and $ g(x) = x^2 - 1 $.

Step 2: Add the Functions

To find $(f+g)(x)$, we add the expressions for $f(x)$ and $g(x)$: \[ (f+g)(x) = f(x) + g(x) = (2x + 3) + (x^2 - 1) \]

Step 3: Simplify the Expression

Combine like terms in the expression: \[ (f+g)(x) = x^2 + 2x + 3 - 1 = x^2 + 2x + 2 \]

Step 4: Evaluate the Expression at $x = 5$

Substitute $x = 5$ into the simplified expression: \[ (f+g)(5) = 5^2 + 2 \times 5 + 2 = 25 + 10 + 2 = 37 \]

The value of $(f+g)(5)$ is $\boxed{37}$.

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