Without using paper and pencil, evaluate each expression given the following functions. $\text{ƒ}\left(x\right)=x+1$ and $g\left(x\right)=x^2$
$(\text{ƒ}-g)\left(2\right)$

Verified step by step guidance

1. Understand that the expression (ƒ - g)(2) means you need to find the value of the function (ƒ - g) at x = 2. The function (ƒ - g)(x) is defined as ƒ(x) - g(x).
2. Write the expression for (ƒ - g)(x) by subtracting g(x) from ƒ(x): (ƒ - g)(x) = ƒ(x) - g(x) = (x + 1) - (x^2).
3. Substitute x = 2 into the expression: (ƒ - g)(2) = (2 + 1) - (2^2).
4. Simplify each part separately: calculate 2 + 1 and 2^2.
5. Subtract the results from the previous step to find the value of (ƒ - g)(2).

Key Concepts

Function Notation and Evaluation

Function notation, such as ƒ(x) and g(x), represents a rule that assigns each input x to an output. Evaluating a function at a specific value means substituting that value into the function's formula 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). To evaluate (ƒ - g)(2), you find ƒ(2) and g(2) separately, then subtract g(2) from ƒ(2). This operation combines functions to create a new function.

Substitution and Simplification

Substitution involves replacing the variable x with a given number in the function's expression. After substitution, simplifying the resulting expression by performing arithmetic operations yields the final value of the function at that point.