INVERSE FUNCTIONS

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 back to x.

Front

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

Back

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

Front

What is the inverse of the function f(x) = 2x + 4?

Back

f^-1(x) = (x - 4) / 2.

Front

If f(x) passes through the point (1, 4), what point does f^-1(x) pass through?

Back

f^-1(x) passes through (4, 1).

Front

What is the inverse of the points (1,3), (2,4), (6,8)?

Back

The inverse points are (3,1), (4,2), (8,6).

Front

What is the graphical representation of inverse functions?

Back

The graph of an inverse function is a reflection of the original function across the line y = x.

Front

What is the relationship between the slopes of a function and its inverse?

Back

If the slope of f(x) at a point is m, then the slope of f^-1(x) at the corresponding point is 1/m.

Front

Can a function have more than one inverse?

Back

No, a function can have at most one inverse unless it is not a one-to-one function.

Front

What is the inverse of the function f(x) = x^2 for x >= 0?

Back

f^-1(x) = √x.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, replace f(x) with y, swap x and y, and solve for y.