Remediation Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the effect 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 can you determine if two functions are inverses?

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 graphical representation of inverse functions?

Back

Inverse functions are reflections of each other across the line y = 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) = x² (for x ≥ 0)?

Back

f⁻¹(x) = √x.

Front

What is the importance of the domain and range in inverse functions?

Back

The domain of the original function becomes the range of the inverse function and vice versa.

Front

How do you find the inverse of a function algebraically?

Back

1. Replace f(x) with y. 2. Swap x and y. 3. Solve for y. 4. Replace y with f⁻¹(x).

Front

What is the inverse of the function f(x) = 10^(3x)?

Back

f⁻¹(x) = (1/3) log(x).

Front

What does it mean if a function does not have an inverse?

Back

A function does not have an inverse if it is not one-to-one, meaning it does not pass the horizontal line test.

Front

What is the horizontal line test?

Back

A function passes the horizontal line test if no horizontal line intersects the graph of the function more than once.