Questions: f(x)=2x+5 g(x)=x+1 Find (f+g)(-9)

Transcript text: $\begin{array}{l}f(x)=2 x+5 \\ g(x)=x+1 \\ \text { Find }(f+g)(-9)\end{array}$

Solution

Solution Steps

To find $(f+g)(-9)$, we need to first determine the expressions for $f(x)$ and $g(x)$. Then, we add these two expressions to get $(f+g)(x)$. Finally, we substitute $-9$ into this new expression to find the result.

Step 1: Define the Functions

We have the functions defined as: \[ f(x) = 2x + 5 \] \[ g(x) = x + 1 \]

Step 2: Find the Sum of the Functions

To find $(f + g)(x)$, we add the two functions: \[ (f + g)(x) = f(x) + g(x) = (2x + 5) + (x + 1) = 3x + 6 \]

Step 3: Evaluate at $x = -9$

Now, we substitute $x = -9$ into the sum: \[ (f + g)(-9) = 3(-9) + 6 = -27 + 6 = -21 \]

Final Answer

The result is $\boxed{-21}$.

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