Composition of function

Front

What is the composition of functions?

Back

The composition of functions is a process where one function is applied to the result 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(3))?

Back

f(g(3)) = f(2*3) = f(6) = 6^2 = 36.

Front

What is the notation for the composition of functions?

Back

The notation for the composition of functions is (f ∘ g)(x), which means f(g(x)).

Front

Given f(x) = x + 1 and g(x) = x^2, find g(f(2)).

Back

g(f(2)) = g(2 + 1) = g(3) = 3^2 = 9.

Front

What is the domain of the composition of functions?

Back

The domain of (f ∘ g) 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 and g(x) = x - 3, what is (f ∘ g)(1)?

Back

(f ∘ g)(1) = f(g(1)) = f(1 - 3) = f(-2) = 2*(-2) = -4.

Front

What is the range of the composition of functions?

Back

The range of (f ∘ g) is the set of all values f(g(x)) can take as x varies over the domain of g.

Front

If f(x) = x^2 + 1 and g(x) = x - 1, find f(g(4)).

Back

f(g(4)) = f(4 - 1) = f(3) = 3^2 + 1 = 10.

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) = 3x + 2 and g(x) = x/2, find g(f(4)).

Back

g(f(4)) = g(3*4 + 2) = g(14) = 14/2 = 7.