Test 4 PreCal - Combinations and Compositions of Functions

Front

What is a function composition?

Back

A function composition is the process of applying one function to the results of another function. It is denoted as (f ° g)(x) = f(g(x)).

Front

What does (f/g)(x) represent?

Back

The expression (f/g)(x) represents the division of two functions f(x) and g(x), defined as f(x) / g(x), provided g(x) ≠ 0.

Front

How do you find h(f(-2)) if h(x) = 3x - 1 and f(x) = x^2 - 1?

Back

First, calculate f(-2): f(-2) = (-2)^2 - 1 = 3. Then, substitute into h: h(3) = 3(3) - 1 = 8.

Front

What is the result of g(h(x)) if g(x) = 3x + 4 and h(x) = 3x - 1?

Back

To find g(h(x)), substitute h(x) into g: g(h(x)) = g(3x - 1) = 3(3x - 1) + 4 = 9x + 1.

Front

What is the value of (f/g)(10) if f(x) = x^2 - 1 and g(x) = x - 1?

Back

Calculate f(10) = 10^2 - 1 = 99 and g(10) = 10 - 1 = 9. Thus, (f/g)(10) = 99 / 9 = 11.

Front

What is the definition of a rational function?

Back

A rational function is a function that can be expressed as the ratio of two polynomials, f(x) = P(x)/Q(x), where Q(x) ≠ 0.

Front

What does it mean for a function to be undefined?

Back

A function is undefined at points where the denominator of a rational function is zero, as division by zero is not possible.

Front

How do you evaluate (h/j)(-2) if h(x) = x^2 - 3x - 10 and j(x) = 3x - 2?

Back

First, calculate h(-2) = (-2)^2 - 3(-2) - 10 = 4 + 6 - 10 = 0. Then, calculate j(-2) = 3(-2) - 2 = -6 - 2 = -8. Thus, (h/j)(-2) = 0 / -8 = 0.

Front

What is the composition of functions f and g if f(x) = x - 5 and g(x) = 3x^2 - 1?

Back

The composition (f ° g)(x) = f(g(x)) = f(3x^2 - 1) = (3x^2 - 1) - 5 = 3x^2 - 6.

Front

What is the domain of a rational function?

Back

The domain of a rational function is all real numbers except where the denominator is zero.