Operations on Functions

Front

What is the definition of function composition?

Back

Function composition is the process of applying one function to the results of another function. If f(x) and g(x) are two functions, then the composition of f and g is denoted as (f ∘ g)(x) = f(g(x)).

Front

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

Back

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

Front

What is the product of two functions?

Back

The product of two functions f(x) and g(x) is defined as (f * g)(x) = f(x) * g(x).

Front

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

Back

(f * g)(x) = (x - 1)(5x - 2) = 5x^2 - 7x + 2.

Front

What is the definition of a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

If p(x) = 3x + 4 and q(x) = 2x^2, what is q(p(-2))?

Back

q(p(-2)) = q(3(-2) + 4) = q(-2) = 2(-2)^2 = 8.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value).

Front

If f(x) = 4x + 8 and g(x) = x + 3, what is (f * g)(x)?

Back

(f * g)(x) = (4x + 8)(x + 3) = 4x^2 + 20x + 24.

Front

What is the definition of a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, and it has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

f(g(3)) = f(2(3)^2 - 1) = f(17) = 2(17) = 34.