For each function, find (a) ƒ(2) and (b) ƒ(-1). See Example 7.

Verified step by step guidance

1. Identify the given function ƒ(x) from the problem statement or example. This function will be used to find the values at specific points.
2. To find ƒ(2), substitute x = 2 into the function. This means replacing every occurrence of x in the function with 2, resulting in the expression ƒ(2) = function evaluated at 2.
3. Simplify the expression obtained after substitution by performing all arithmetic operations and applying any trigonometric identities if necessary, but do not calculate the final numeric value yet.
4. To find ƒ(-1), substitute x = -1 into the function. Replace every x in the function with -1, resulting in the expression ƒ(-1) = function evaluated at -1.
5. Simplify the expression obtained after substituting x = -1 by performing all arithmetic operations and applying any trigonometric identities if necessary, again without calculating the final numeric value.

Key Concepts

Function Evaluation

Function evaluation involves substituting a given input value into the function's formula to find the corresponding output. For example, to find ƒ(2), replace the variable with 2 and simplify the expression to get the result.

Understanding Function Notation

Function notation, such as ƒ(x), represents a function named ƒ with input variable x. Recognizing this notation helps in correctly substituting values and interpreting the function's behavior at specific points.

Handling Negative Inputs in Functions

When evaluating functions at negative inputs like ƒ(-1), it is important to carefully substitute the negative value and apply algebraic rules correctly, especially with powers and signs, to avoid errors in simplification.