Function Composition and 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(0)) if f(x) = 3x + 10 and g(x) = x - 2?

Back

First, find g(0): g(0) = 0 - 2 = -2. Then, find f(-2): f(-2) = 3(-2) + 10 = 4.

Front

What is the formula for adding two functions f and g?

Back

The formula for adding two functions is (f + g)(x) = f(x) + g(x).

Front

If f(x) = 3x^2 + 1 and g(x) = 4x + 5, what is (f + g)(2)?

Back

(f + g)(2) = f(2) + g(2) = (3(2^2) + 1) + (4(2) + 5) = 26.

Front

What does (h/j)(-2) mean if h(x) = x^2 - 3x - 10 and j(x) = 3x - 2?

Back

(h/j)(-2) means to evaluate h(-2) and j(-2) and then divide the results: h(-2) = 0 and j(-2) = -8, so (h/j)(-2) = 0.

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 and n is a non-negative integer.

Front

How do you find q(p(-2)) if p(x) = 3x + 4 and q(x) = 2x^2?

Back

First, find p(-2): p(-2) = 3(-2) + 4 = -2. Then, find q(-2): q(-2) = 2(-2)^2 = 8.

Front

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

Back

f(g(x)) applies g first and then f, while g(f(x)) applies f first and then g. They are generally not equal unless f and g have specific properties.

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.