Inverse Function Practice

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) takes an input x and produces an output y, then the inverse function f^{-1}(y) takes y as input and produces x as output.

Front

How do you find the inverse of a linear function?

Back

To find the inverse of a linear function, swap the x and y variables and solve for y. For example, for T(x) = 6x - 7, swap to get x = 6y - 7, then solve for y.

Front

What is the inverse of T(x) = 6x - 7?

Back

T^{-1}(x) = (x + 7) / 6.

Front

What is the inverse of f(x) = 10 + 7x?

Back

f^{-1}(x) = (x - 10) / 7.

Front

How do you verify if two functions are inverses?

Back

To verify if f and g are inverses, check if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Front

What is the inverse of f(x) = (3x + 10) / 7?

Back

f^{-1}(x) = (7x - 10) / 3.

Front

What is the inverse of f(x) = 4x?

Back

f^{-1}(x) = x / 4.

Front

What is the significance of the horizontal line test in relation to inverse functions?

Back

The horizontal line test determines if a function is one-to-one. If any horizontal line intersects the graph of the function more than once, the function does not have an inverse.

Front

What is the general form of a linear function?

Back

The general form of a linear function is f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements, meaning each output is produced by exactly one input.