inverses
What is the primary characteristic of an inverse function regarding its inputs and outputs?
It swaps the domain (inputs) and range (outputs) of the original function.
According to the product rule, what is xᵃ · xᵇ?
xᵃ⁺ᵇ
How do you calculate the average rate of change of a function between two points (x₁, y₁) and (x₂, y₂)?
The slope formula: (y₂ - y₁) / (x₂ - x₁)
If f(x) = 3x - 6, what is its inverse function f⁻¹(x)?
f⁻¹(x) = (x + 6) / 3
According to the quotient rule, what is xᵃ / xᵇ (for x ≠ 0)?
xᵃ⁻ᵇ
What is the simplified form of √75?
5√3
When verifying that two functions are inverses using composition, what must f(f⁻¹(x)) always equal?
x
According to the power of a power rule, what is (xᵃ)ᵇ?
xᵃᵇ
How do you set up the average rate of change of f(x) over the interval [a, b]?
(f(b) - f(a)) / (b - a)
What is the inverse of f(x) = x² restricted to the domain x ≥ 0?
f⁻¹(x) = √x
What is the value of any non-zero base raised to the zero power, x⁰?
1
What is the simplified form of the radical expression √x⁵?
x²√x
What is the inverse of the rational function f(x) = (2x + 1) / (x - 3)?
f⁻¹(x) = (3x + 1) / (x - 2)
Simplify the expression using exponent properties: (2x³)² · x⁴
4x¹⁰
Simplify and combine: √12 + √27
5√3