The problem in the image asks to perform operations on given functions $f(x)$, $g(x)$, and $h(x)$. The functions provided are:

• $f(x) = x^2 - 3x + 4$
• $g(x) = 5x + 2$
• $h(x) = 6x$

Let's perform the operations for parts a and b:

a. $(f + g)(x)$

This means we need to add the two functions $f(x)$ and $g(x)$:

$(f + g)(x) = f(x) + g(x)$

Substituting the given functions:

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

Now, combine like terms:

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

$(f + g)(x) = x^2 + 2x + 6$

b. $(f - g)(x)$

This means we need to subtract the function $g(x)$ from $f(x)$:

$(f - g)(x) = f(x) - g(x)$

Substituting the given functions:

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

Distribute the negative sign and combine like terms:

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

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

$(f - g)(x) = x^2 - 8x + 2$

Summary:

• $(f + g)(x) = x^2 + 2x + 6$
• $(f - g)(x) = x^2 - 8x + 2$

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you find the product of two functions, such as $(f \times g)(x)$?
2. What is the composition of two functions, such as $(f \circ g)(x)$?
3. How would the operation $(f + h)(x)$ look?
4. Can you calculate $(g - h)(x)$?
5. How do you simplify $(f \times g)(x)$?

Tip: Always combine like terms when performing function addition or subtraction!