Operations and Composition of Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

Front

What is function composition?

Back

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

Front

How do you find g(h(x)) if g(x) = 3x + 4 and h(x) = 3x - 1?

Back

g(h(x)) = g(3x - 1) = 3(3x - 1) + 4 = 9x - 3 + 4 = 9x + 1.

Front

What is the restriction for the function f(x)/g(x) if f(x) = 3x^2 - 2x + 1 and g(x) = x - 4?

Back

The restriction is x ≠ 4, as g(x) cannot be zero.

Front

How do you find f(g(x)) if f(x) = 2x and g(x) = x^2 + 3?

Back

f(g(x)) = f(x^2 + 3) = 2(x^2 + 3) = 2x^2 + 6.

Front

What is the result of f(x) - g(x) if f(x) = x^2 + 9 and g(x) = x - 9?

Back

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

Front

What is the value of g(h(1)) if g(a) = 4a + 1 and h(a) = -3a + 2?

Back

g(h(1)) = g(-3(1) + 2) = g(-1) = 4(-1) + 1 = -4 + 1 = -3.

Front

What is the domain of a function?

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

What does it mean for two functions to be equal?

Back

Two functions f(x) and g(x) are equal if they produce the same output for every input in their common domain.