IM Unit 4 Lessons 15-17 Inverse Functions

Front

What is the definition of an inverse function?

Back

An inverse function reverses the operation of the original function. If the function f takes an input x to produce an output y, then the inverse function f⁻¹ takes y back to 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

If f(x) = 3x, what is the inverse?

Back

Front

Back

Front

What is the first step in finding the inverse of the function y = 3x + 4?

Back

Subtract 4 from both sides to isolate the term with x.

Front

Was the inverse function found correctly for y = 3x + 4?

Back

Front

Are the functions y = -7x - 4 and x = -\frac{1}{7}y - \frac{4}{7} inverses of each other?

Back

Yes, they are inverse functions.

Front

Are the functions y = 3 - \frac{1}{2}x and x = -2y + 6 inverses of each other?

Back

Yes, they are inverse functions.

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 a function and its inverse regarding their outputs?

Back

If f(a) = b, then f⁻¹(b) = a.