Let f(x)=2^x . We will see in the next section that this function is one-toone. Find each value,

step 1 Part A is asking what is F of negative 2? So we're plugging in that negative 2 into x. So F of n

Let f(x)=2^x . We will see in the next section that this...

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Key Concepts

Properties of Exponents

The properties of exponents govern the manipulation and evaluation of expressions involving powers. One key property is that a negative exponent, such as a??, is defined as 1/(a?) when a is a nonzero number. These rules are essential for simplifying and evaluating expressions in exponential functions.

One-to-One Functions

One-to-one functions have a unique feature where every element in the range is associated with exactly one element in the domain. This injectivity is critical because it ensures that the function has an inverse, allowing us to reverse the mapping from outputs back to their corresponding inputs.

Exponential Functions

Exponential functions are mathematical expressions where the variable appears in the exponent, typically taking the form f(x) = b^x with a positive base b. These functions exhibit rapid growth or decay and are fundamental in modeling phenomena such as population growth, radioactive decay, and compound interest.

Inverse Functions

An inverse function reverses the operation of the original function by swapping its inputs and outputs. For a function f, the inverse f?¹, if it exists, satisfies the condition f(f?¹(y)) = y and f?¹(f(x)) = x. Inverse functions are particularly useful when we need to determine the input corresponding to a given output.

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