Finding Inverse Equations Practice

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) = y, then the inverse function 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 in the equation and solve for y.

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

What is the notation for an inverse function?

Back

The notation for an inverse function is f⁻¹(x), where f is the original function.

Front

What is the first step in finding the inverse of the function f(x) = 2x + 3?

Back

The first step is to replace f(x) with y: y = 2x + 3.

Front

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

Back

To verify, check if f(f⁻¹(x)) = x and f⁻¹(f(x)) = x for all x in the domain.

Front

What is the inverse of the function f(x) = x² for x ≥ 0?

Back

The inverse is f⁻¹(x) = √x, since we restrict x to non-negative values.

Front

What is the domain of the inverse function if the original function is f(x) = 1/x?

Back

The domain of the inverse function f⁻¹(x) = 1/x is all real numbers except 0.

Front

What is the significance of the horizontal line test?

Back

The horizontal line test determines if a function is one-to-one, which is necessary for it to have an inverse.

Front

How do you find the inverse of a linear function?

Back

For a linear function f(x) = mx + b, the inverse is f⁻¹(x) = (x - b)/m.