composition of functions+function operations

Front

What is the composition of functions?

Back

The composition of functions is a way to combine two functions, where the output of one function becomes the input of another. It is denoted as (f ∘ g)(x) = f(g(x)).

Front

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

Back

(f ∘ g)(2) = f(g(2)) = f(2 + 3) = f(5) = 2(5) = 10.

Front

Define the term 'function operation'.

Back

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

Front

What is the result of (g ∘ f)(x) if f(x) = x^2 and g(x) = 3x?

Back

(g ∘ f)(x) = g(f(x)) = g(x^2) = 3(x^2) = 3x^2.

Front

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

Back

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

Front

What is the formula for the composition of two functions f and g?

Back

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

Front

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

Back

(f ∘ g)(-1) = f(g(-1)) = f(-1 + 1) = f(0) = 0^2 = 0.

Front

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

Back

f(g(x)) is the composition of f and g, where g is applied first, while g(f(x)) is the composition where f is applied first. They may yield different results.

Front

If f(x) = 1/x and g(x) = 3x + 2, find (f ∘ g)(2).

Back

(f ∘ g)(2) = f(g(2)) = f(3(2) + 2) = f(8) = 1/8.

Front

What is the result of (g ∘ g)(-4) if g(x) = 3x + 2?

Back

(g ∘ g)(-4) = g(g(-4)) = g(3(-4) + 2) = g(-10) = 3(-10) + 2 = -28.