Composition of Functions

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

If f(x) = x^2 and g(x) = √x, what is g(f(x))?

Back

g(f(x)) = g(x^2) = √(x^2) = x.

Front

What is the formula for the composition of functions?

Back

The formula for the composition of functions is (f ∘ g)(x) = f(g(x)).

Front

If f(x) = x^2 + 9 and g(x) = x - 9, what is f(x) - g(x)?

Back

f(x) - g(x) = (x^2 + 9) - (x - 9) = x^2 - x + 18.

Front

If f(x) = 9 - 3x and g(x) = 5x - 7, what is f(x) + g(x)?

Back

f(x) + g(x) = (9 - 3x) + (5x - 7) = 2x + 2.

Front

What is the result of g(f(x)) if g(x) = x^2 + 6 and f(x) = 2x - 4?

Back

g(f(x)) = g(2x - 4) = (2x - 4)^2 + 6 = 4x^2 - 16x + 22.

Front

If f(x) = 2x^2 - 5x + 1 and g(x) = x^(1/2) + 3, what is f(g(x))?

Back

f(g(x)) = f(x^(1/2) + 3) = 2(x^(1/2) + 3)^2 - 5(x^(1/2) + 3) + 1 = 2x + 7x^(1/2) + 4.

Front

What is the domain of the function g(x) = √x?

Back

The domain of g(x) = √x is x ≥ 0, since the square root of a negative number is not defined in the set of real numbers.

Front

What is the range of the function f(x) = x^2?

Back

The range of f(x) = x^2 is y ≥ 0, as the output of a square function is always non-negative.

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.