function composition

Front

What is function composition?

Back

Function composition is the process of applying one function to the results of another function. It is denoted as (f ° g)(x) = f(g(x)).

Front

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

Back

f(g(x)) = f(2x) = (2x)^2 = 4x^2.

Front

What is the notation for function composition?

Back

The notation for function composition is (f ° g)(x), which means f applied to g of x.

Front

If f(x) = 3x + 1 and g(x) = x - 4, what is (f ° g)(x)?

Back

(f ° g)(x) = f(g(x)) = f(x - 4) = 3(x - 4) + 1 = 3x - 12 + 1 = 3x - 11.

Front

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

Back

g(f(x)) = g(x + 2) = (x + 2)^2 = x^2 + 4x + 4.

Front

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

Back

(f ° g)(x) = f(g(x)) = f(3x^2 - 1) = (3x^2 - 1) - 5 = 3x^2 - 6.

Front

What is the domain of the composition of functions?

Back

The domain of (f ° g)(x) is the set of all x in the domain of g such that g(x) is in the domain of f.

Front

If f(x) = 2x + 3 and g(x) = x^2, what is (g ° f)(x)?

Back

(g ° f)(x) = g(f(x)) = g(2x + 3) = (2x + 3)^2 = 4x^2 + 12x + 9.

Front

What is the difference between f(g(x)) and g(f(x))?

Back

f(g(x)) applies g first and then f, while g(f(x)) applies f first and then g. They are generally not equal.

Front

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

Back

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