Function Operations and compositions

Front

What is the sum of two functions f(x) and g(x)?

Back

(f + g)(x) = f(x) + g(x)

Front

Given f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, find (f + g)(x).

Back

(f + g)(x) = 5x^2 + 6x - 1

Front

What is function composition?

Back

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

Front

Given f(x) = 3x + 10 and g(x) = x - 2, find f(g(0)).

Back

f(g(0)) = f(-2) = 4.

Front

What is the difference of two functions f(x) and g(x)?

Back

(f - g)(x) = f(x) - g(x)

Front

Given f(x) = x^2 + 1 and g(x) = 2x - 5, find f(x) - g(x).

Back

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

Front

What is the product of two functions f(x) and g(x)?

Back

(f * g)(x) = f(x) * g(x)

Front

Given p(x) = 3x + 4 and q(x) = 2x^2, find q(p(-2)).

Back

q(p(-2)) = q(-2) = 8.

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_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0, where a_n, a_{n-1}, ..., a_0 are constants.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable x in the polynomial.