Composition of Functions

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) = 3x, what is g(f(1))?

Back

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

Front

Define the term 'domain' in the context of functions.

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

If f(x) = 2x - 3, what is f(4)?

Back

f(4) = 2(4) - 3 = 8 - 3 = 5.

Front

What does it mean for a function to be 'undefined'?

Back

A function is undefined at a certain point if there is no output value for that input, often due to division by zero or taking the square root of a negative number.

Front

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

Back

(g ∘ f)(2) = g(f(2)) = g(2^2) = g(4) = 4 + 1 = 5.

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

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

Back

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

Front

What is the inverse of a function?

Back

The inverse of a function f(x) is a function that reverses the effect of f, denoted as f^(-1)(x). It satisfies the condition f(f^(-1)(x)) = x.