HW 1.8A

Front

What is function composition and how is it denoted?

Back

Function composition is the process of applying one function to the results of another function. It is denoted as g(f(x)), meaning you first apply f to x, then apply g to the result of f(x).

Front

Given f(x) = 2x - 8 and g(x) = 4x, what is g(f(x))?

Back

g(f(x)) = g(2x - 8) = 4(2x - 8) = 8x - 32.

Front

How do you find the sum of two functions, (f + g)(x)?

Back

To find the sum of two functions, you add their outputs: (f + g)(x) = f(x) + g(x).

Front

If f(x) = x^2 + 25 and g(x) = x - 5, what is (f + g)(x)?

Back

(f + g)(x) = (x^2 + 25) + (x - 5) = x^2 + x + 20.

Front

What is the process to find f(g(x))?

Back

To find f(g(x)), substitute g(x) into f(x).

Front

Given f(x) = 3x + 10 and g(x) = x - 2, what is f(g(5))?

Back

g(5) = 5 - 2 = 3, then f(g(5)) = f(3) = 3(3) + 10 = 19.

Front

How do you find the difference of two functions, (f - g)(x)?

Back

To find the difference of two functions, you subtract their outputs: (f - g)(x) = f(x) - g(x).

Front

If f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, what is (f - g)(x)?

Back

(f - g)(x) = (3x^2 + 7x) - (2x^2 - x - 1) = x^2 + 8x + 1.

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

What is the significance of the degree of a polynomial?

Back

The degree of a polynomial indicates the highest power of the variable in the polynomial and determines the polynomial's end behavior and the number of roots it can have.