composition of functions+function operations

Front

What is a function composition?

Back

Function composition is the process of applying one function to the results of another function. If you have two functions, f(x) and g(x), the composition is denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you find (f ∘ g)(x) if f(x) = 2x and g(x) = 2x^2 - 1?

Back

To find (f ∘ g)(x), substitute g(x) into f: (f ∘ g)(x) = f(g(x)) = f(2x^2 - 1) = 2(2x^2 - 1) = 4x^2 - 2.

Front

What is the result of g(f(-1)) if f(x) = 2x and g(x) = 2x^2 - 1?

Back

First, find f(-1): f(-1) = 2(-1) = -2. Then, find g(-2): g(-2) = 2(-2)^2 - 1 = 8 - 1 = 7.

Front

What is the formula for (f ∘ g)(x) if f(x) = 1/x and g(x) = 3x + 2?

Back

(f ∘ g)(x) = f(g(x)) = f(3x + 2) = 1/(3x + 2).

Front

How do you calculate (f ∘ g)(2) if f(x) = 1/x and g(x) = 3x + 2?

Back

First, find g(2): g(2) = 3(2) + 2 = 8. Then, find f(8): f(8) = 1/8.

Front

What is the product of two functions f(x) = 2x + 3 and g(x) = -3x - 4?

Back

The product is f(x) * g(x) = (2x + 3)(-3x - 4) = -6x^2 - 17x - 12.

Front

Define the term 'function operation'.

Back

Function operations refer to the various ways functions can be combined, including addition, subtraction, multiplication, and composition.

Front

What is the result of (f + g)(x) if f(x) = 2x and g(x) = 2x^2 - 1?

Back

(f + g)(x) = f(x) + g(x) = 2x + (2x^2 - 1) = 2x^2 + 2x - 1.

Front

What does it mean for two functions to be 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

How do you find the inverse of a function?

Back

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