U12 Topic 1 Practice: Writing Inverses

Front

What is the notation for the inverse of a function?

Back

f^{-1}(x)

Front

How do you find the inverse of a function?

Back

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

Front

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

Back

f^{-1}(x) = (x - 3)/2

Front

If f(x) = 5x - 7, what is f^{-1}(x)?

Back

f^{-1}(x) = (x + 7)/5

Front

What is the inverse of f(x) = -4x - 12?

Back

f^{-1}(x) = -1/4x - 3

Front

What does it mean for two functions to be inverses of each other?

Back

If f and g are inverses, then f(g(x)) = x and g(f(x)) = x.

Front

What is the graphical representation of a function and its inverse?

Back

The graph of a function and its inverse are reflections over the line y = x.

Front

How do you verify if two functions are inverses?

Back

Substitute one function into the other; if both compositions equal x, they are inverses.

Front

What is the inverse of f(x) = 3x + 15?

Back

f^{-1}(x) = (x - 15)/3

Front

What is the significance of the slope in a linear function's inverse?

Back

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