How is the inverse f⁻¹(x) of a function f(x) defined?
f⁻¹(f(x)) = x for all x∈D(f)
What is the domain of f⁻¹(x)?
the range of f(x)
What is the range of f⁻¹(x)?
the domain of f(x)
What must be true of f(x) for it to be a one-to-one function?
f(a)=f(b)→a=b {a,b∈D(f))
f(a)=f(b) implies a=b for all a,b∈D(f)
What is the Horizontal Line Test?
A method to determine if an graph’s inverse is a function, performed by checking whether every possible horizontal line intersects the graph at exactly one point
If f(x) is one-to-one, what can be said of f⁻¹(x)?
f⁻¹(x) is one-to-one
What are the cancellation equations for inverse functions?
f⁻¹(f(x)) = x for all x∈D(f)
f(f⁻¹(x)) = x for all x∈R(f)
How can you find f⁻¹(x) if you know f(x)?
Swap out x for f⁻¹(x) and swap out f(x) for x, then solve for f⁻¹(x).
The graph of f⁻¹(x) is always the same as the graph of f(x) mirrored over the line…
y = x
If f(x) is a one-to-one function, and g(x) = f(x)+k, then g⁻¹(x) = …
f⁻¹(x-k)
How is log{a, x} defined?
such that log{a, (a^x)}=x
How is ln(x) defined?
log{e, x}
{1, x ∫ {1/t}dt }
What is the equation “log{b, a} = c” in exponential form?
b^c = a
What is the equation “b^c = a” in logarithmic form?
log{b, a} = c
What is logarithmic differentiation?
A method of taking the natural logarithm of both sides of an equation to make it easier to find the derivative of a function
