CH 5 Inverse Functions

Front

What is the definition of an inverse function?

Back

An inverse function reverses the operation of the original function, meaning if the function f takes an input x to an output y, then the inverse function f^{-1} takes y back to 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 in the equation and solve for y.

Front

Evaluate: log 1000

Back

3

Front

Find the inverse function of f(x) = 5^(x+3) - 2.

Back

f^{-1}(x) = log_5(x + 2) - 3.

Front

Find the inverse of: y = log_9(x) + 4. HINT: isolate the logarithm first.

Back

y = 9^(x - 4).

Front

What does it mean to find the inverse of a function?

Back

The x's and y's are switched.

Front

Which function represents the inverse of the function f(x) = -3x + 4?

Back

g(x) = (x - 4)/-3.

Front

What is the relationship between a function and its inverse?

Back

The graph of a function and its inverse are reflections of each other across the line y = x.

Front

If f(x) = 2x + 3, what is f^{-1}(x)?

Back

f^{-1}(x) = (x - 3)/2.

Front

What is the domain of the inverse function if the original function has a range of [0, ∞)?

Back

The domain of the inverse function will be [0, ∞).