Inverses Advanced Algebra

Front

What is the definition of an inverse function?

Back

An inverse function reverses the operation of the original function, such that if f(x) = y, then f^-1(y) = x.

Front

How do you find the inverse of a function?

Back

1. Replace f(x) with y. 2. Switch x and y. 3. Solve for y. 4. Replace y with f^-1(x).

Front

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

Back

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

Front

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

Back

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

Front

Are the functions f(x) = 2x + 1 and g(x) = (x - 1)/2 inverses of each other?

Back

Yes, because g(f(x)) = x and f(g(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

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

Back

The slope of the inverse function is the reciprocal of the slope of the original function.

Front

If f(x) = x^2, what is the inverse function?

Back

f^-1(x) = √x (for x ≥ 0).

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, ∞) if the original function has a range of [0, ∞).

Front

What is the importance of one-to-one functions in finding inverses?

Back

Only one-to-one functions have inverses that are also functions, as they pass the horizontal line test.