Given the definitions of f, of, xf(x) and g, of, xg(x) below, find the value of f, of, g, of, 0, .f(g(0)).
f, of, x, equals, 2, x, squared, minus, 5, x, plus, 12
f(x)=
2x 
2
 −5x+12
g, of, x, equals, minus, 3, x, minus, 3
g(x)=
−3x−3

To find \( f(g(0)) \), we need to first evaluate \( g(0) \) and then substitute that result into the function \( f(x) \).

### Step 1: Find \( g(0) \)
The function \( g(x) \) is given as:
\[
g(x) = -3x - 3
\]
Substitute \( x = 0 \):
\[
g(0) = -3(0) - 3 = -3
\]

### Step 2: Substitute \( g(0) \) into \( f(x) \)
Now, substitute \( g(0) = -3 \) into the function \( f(x) \). The function \( f(x) \) is:
\[
f(x) = 2x^2 - 5x + 12
\]
Substitute \( x = -3 \):
\[
f(-3) = 2(-3)^2 - 5(-3) + 12
\]
Now, simplify the expression:
\[
f(-3) = 2(9) + 15 + 12 = 18 + 15 + 12 = 45
\]

Thus, \( f(g(0)) = 45 \).

### Final Answer:
\[
f(g(0)) = 45
\]

Would you like more details on any part of the solution?

Here are 5 questions related to this:

1. What happens if the function \( g(x) \) changes?
2. How would the answer differ if \( f(x) \) were linear instead of quadratic?
3. What are other techniques for combining functions?
4. How do you graph the composition of two functions?
5. How does changing the variable in one function affect the composition?

**Tip**: When composing functions, always solve the inner function first before plugging the result into the outer function.

Given the definitions of f(x) = 2x^2 - 5x + 12 and g(x) = -3x - 3, find the value of f(g(0)).

Learn how to solve the function composition f(g(0)) where f(x) = 2x^2 - 5x + 12 and g(x) = -3x - 3. This problem illustrates the process of finding the value of the composed function step-by-step, covering key concepts in algebra and quadratic functions. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation