If f(x)=x2−4xf(x)=x2−4x and g(x)=3x+5g(x)=3x+5, find f(3)+g(−5)


Let's solve the given problem step by step.

We are given the functions:

- \( f(x) = x^2 - 4x \)
- \( g(x) = 3x + 5 \)

We need to find \( f(3) + g(-5) \).

### Step 1: Calculate \( f(3) \)
Substitute \( x = 3 \) into the function \( f(x) \):

\[
f(3) = 3^2 - 4(3)
\]
\[
f(3) = 9 - 12 = -3
\]

### Step 2: Calculate \( g(-5) \)
Substitute \( x = -5 \) into the function \( g(x) \):

\[
g(-5) = 3(-5) + 5
\]
\[
g(-5) = -15 + 5 = -10
\]

### Step 3: Add \( f(3) \) and \( g(-5) \)
Now, we add the results from steps 1 and 2:

\[
f(3) + g(-5) = -3 + (-10) = -13
\]

So, the value of \( f(3) + g(-5) \) is \( \boxed{-13} \).

Would you like further clarification or additional questions? Here are some related topics for exploration:

1. How do we compute the value of functions at specific points?
2. What are the properties of quadratic functions like \( f(x) = x^2 - 4x \)?
3. How do linear functions like \( g(x) = 3x + 5 \) behave differently from quadratic ones?
4. What does the graph of \( f(x) = x^2 - 4x \) look like?
5. How do you evaluate the sum of two functions at specific points?

**Tip:** When adding or subtracting functions at specific values, remember to evaluate each function separately at the given point and then combine the results.

If f(x) = x^2 − 4x and g(x) = 3x + 5, find f(3) + g(−5)

Learn how to evaluate the functions f(x) = x^2 - 4x and g(x) = 3x + 5 at specific points and find f(3) + g(-5) with a step-by-step solution. This problem covers function evaluation, algebraic manipulation, and quadratic function concepts. Suitable for students in Grades 8-10.

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