Without using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1 and g(x)=x^2 (ƒ-g)(2)

Verified step by step guidance

1. Identify the functions: $f(x)=x+1$ and $g(x)=x^2$.
2. Understand that $(f-g)(x)$ means $f(x)-g(x)$.
3. Substitute the expressions for $f(x)$ and $g(x)$ into $(f-g)(x)$: $(f-g)(x)=(x+1)-(x^2)$.
4. Substitute $x=2$ into the expression: $(f-g)(2)=(2+1)-(2^2)$.
5. Simplify the expression by performing the arithmetic operations: $(f-g)(2)=3-4$.

Key Concepts

Function Notation

Function notation is a way to represent mathematical functions in a clear and concise manner. In this case, ƒ(x) and g(x) denote two different functions, where ƒ(x) = x + 1 and g(x) = x². Understanding how to read and interpret these notations is essential for evaluating expressions involving these functions.

Function Operations

Function operations involve combining functions through addition, subtraction, multiplication, or division. The expression (ƒ - g)(x) represents the difference between the two functions ƒ and g. To evaluate (ƒ - g)(2), one must first compute ƒ(2) and g(2), then subtract the results to find the final value.

Evaluating Functions

Evaluating functions means substituting a specific value into the function to find its output. For example, to evaluate ƒ(2) and g(2), you replace x with 2 in their respective equations. This process is crucial for solving the expression (ƒ - g)(2) and obtaining the correct numerical result.