Chapter 5 Review: Inverses

Front

What is the definition of an inverse function?

Back

An inverse function reverses the operation of the original function, such that if f(x) = y, then f^(-1)(y) = x.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse of a function, swap the x and y variables and solve for y.

Front

What is the inverse of the exponential function y = a^x?

Back

The inverse of the exponential function y = a^x is y = log_a(x).

Front

What is the relationship between logarithmic and exponential functions?

Back

Logarithmic functions are the inverses of exponential functions, meaning if y = log_a(x), then x = a^y.

Front

How do you express log_a(b) in exponential form?

Back

log_a(b) = c can be expressed in exponential form as a^c = b.

Front

What is the inverse of the function f(x) = (6x/5) + 3?

Back

The inverse function is f^(-1)(x) = (5(x - 3))/6.

Front

What is the inverse of the function y = log_4(x - 1)?

Back

The inverse function is y = 4^x + 1.

Front

How do you determine if two functions are inverses of each other?

Back

Two functions f and g are inverses if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain a given number, denoted as log_b(a) where b is the base.

Front

What is the domain of a logarithmic function?

Back

The domain of a logarithmic function is the set of positive real numbers (x > 0).