Given the functions:

• $f(x) = x + 3$
• $g(x) = 2x + 7$
• $h(x) = x^2$

Here are some operations you can perform with these functions:

1. Addition of Functions: $(f + g)(x) = f(x) + g(x) = (x + 3) + (2x + 7) = 3x + 10$ $(f + h)(x) = f(x) + h(x) = (x + 3) + x^2 = x^2 + x + 3$

2. Subtraction of Functions: $(f - g)(x) = f(x) - g(x) = (x + 3) - (2x + 7) = -x - 4$ $(h - g)(x) = h(x) - g(x) = x^2 - (2x + 7) = x^2 - 2x - 7$

3. Multiplication of Functions: $(f \cdot g)(x) = f(x) \cdot g(x) = (x + 3)(2x + 7) = 2x^2 + 7x + 6x + 21 = 2x^2 + 13x + 21$ $(f \cdot h)(x) = f(x) \cdot h(x) = (x + 3) \cdot x^2 = x^3 + 3x^2$

4. Division of Functions: $\left(\frac{f}{g}\right)(x) = \frac{f(x)}{g(x)} = \frac{x + 3}{2x + 7}$ $\left(\frac{h}{f}\right)(x) = \frac{h(x)}{f(x)} = \frac{x^2}{x + 3}$

5. Composition of Functions: $(f \circ g)(x) = f(g(x)) = f(2x + 7) = (2x + 7) + 3 = 2x + 10$ $(h \circ f)(x) = h(f(x)) = h(x + 3) = (x + 3)^2 = x^2 + 6x + 9$

Would you like more details or have any questions?

Related Questions:

1. How do you find the inverse of these functions?
2. What is the domain and range of each function?
3. How would you graph these functions on the same coordinate plane?
4. What are the zeros (roots) of each function?
5. How do these functions behave as $x$ approaches infinity?

Tip:

When composing functions, always be careful with the order; $f \circ g$ is generally different from $g \circ f$.