Composition & Inverse Functions

Front

What is a composition of functions?

Back

The composition of functions, denoted as (f ° g)(x), is the application of one function to the results of another function. It means you apply g first, then apply f to the result.

Front

If f(x) = 2x + 3, what is f(2)?

Back

f(2) = 2(2) + 3 = 7.

Front

What is the inverse of a function?

Back

The inverse of a function f, denoted as f^-1, is a function that reverses the effect of f. If f(x) = y, then f^-1(y) = 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

What is the relationship between a function and its inverse?

Back

A function and its inverse are reflections of each other over the line y = x.

Front

If f(1) = 4, what is f^-1(4)?

Back

f^-1(4) = 1.

Front

What does it mean for two functions to be inverses?

Back

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

Front

If g(x) = x² + 2, what is g(3)?

Back

g(3) = 3² + 2 = 11.

Front

What is the graphical representation of a function's inverse?

Back

The graph of a function's inverse is obtained by reflecting the graph of the function over the line y = x.

Front

If f(x) = 3x - 1, what is (f ° g)(x) if g(x) = x² + 2?

Back

(f ° g)(x) = f(g(x)) = f(x² + 2) = 3(x² + 2) - 1 = 3x² + 5.