Let $\text{ƒ}\left(x\right)=x^2+3$ and $g\left(x\right)=-2x+6$. Find each of the following. See Example 1.
$(\text{ƒ}-g)\left(4\right)$

Verified step by step guidance

1. Understand that the expression (ƒ - g)(4) means you need to find the value of the function ƒ(x) minus the function g(x) when x = 4. In other words, (ƒ - g)(4) = ƒ(4) - g(4).
2. Calculate ƒ(4) by substituting x = 4 into the function ƒ(x) = x^2 + 3. This gives ƒ(4) = 4^2 + 3.
3. Calculate g(4) by substituting x = 4 into the function g(x) = -2x + 6. This gives g(4) = -2(4) + 6.
4. Subtract the value of g(4) from ƒ(4) to find (ƒ - g)(4). So, (ƒ - g)(4) = ƒ(4) - g(4).
5. Simplify the expression from the previous step to get the final value of (ƒ - g)(4).

Key Concepts

Function Notation and Evaluation

Function notation, such as ƒ(x), represents a rule that assigns each input x to an output value. Evaluating a function at a specific value means substituting that value into the function's expression and simplifying to find the output.

Function Operations (Difference of Functions)

The difference of two functions (ƒ - g)(x) is defined as ƒ(x) minus g(x). This operation creates a new function by subtracting the output of g from the output of ƒ for the same input x.

Substitution and Simplification

To find (ƒ - g)(4), substitute x = 4 into both ƒ(x) and g(x), then subtract the results. Simplifying the expressions after substitution yields the final numerical value.