Function Operations

Front

What is 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)).

Front

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

Back

To find f(g(x)), substitute g(x) into f(x): f(g(x)) = f(x^2 + 3) = 2(x^2 + 3) = 2x^2 + 6.

Front

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

Back

The result of multiplying two functions f(x) and g(x) is given by (f * g)(x) = f(x) * g(x).

Front

If f(x) = 3 and g(x) = 6x + 4, what is f(x) * g(x)?

Back

f(x) * g(x) = 3 * (6x + 4) = 18x + 12.

Front

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

Back

The sum of two functions f(x) and g(x) is given by (f + g)(x) = f(x) + g(x).

Front

If f(x) = 9 - 3x and g(x) = 5x - 7, what is f(x) + g(x)?

Back

f(x) + g(x) = (9 - 3x) + (5x - 7) = 2x + 2.

Front

How do you find f(g(4)) if f(x) = x^2 + x and g(x) = 3x + 1?

Back

First, find g(4): g(4) = 3(4) + 1 = 13. Then, find f(13): f(13) = 13^2 + 13 = 182.

Front

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

Back

The difference between two functions f(x) and g(x) is given by (f - g)(x) = f(x) - g(x).

Front

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

Back

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

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.