Inverse Linear Functions

Front

What is an inverse function?

Back

An inverse function reverses the effect of the original function. If f(x) takes x to y, then f⁻¹(y) takes y back to x.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, swap x and y in the equation and solve for y.

Front

What is the inverse of the function f(x) = 2x + 3?

Back

f⁻¹(x) = (x - 3)/2.

Front

Are the functions f(x) = 2x + 3 and g(x) = (x - 3)/2 inverses of each other?

Back

Yes, they are inverses because f(g(x)) = x and g(f(x)) = x.

Front

What is the graphical representation of inverse functions?

Back

The graphs of inverse functions are reflections of each other across the line y = x.

Front

If f(x) = 3x - 5, what is f⁻¹(2)?

Back

f⁻¹(2) = (2 + 5)/3 = 7/3.

Front

What is the inverse of the coordinates (4, 5)?

Back

The inverse is (5, 4).

Front

How can you tell if two functions are inverses by their graphs?

Back

If the graphs intersect the line y = x at all points, they are inverses.

Front

What is the inverse of f(x) = 1/2x + 1?

Back

f⁻¹(x) = 2(x - 1).

Front

What does it mean if two functions are not inverses?

Back

It means that applying one function after the other does not return the original input.