Composite Functions Flashcards
Let f(x) = 2x and g(x) = x^2. How will the equation of f(g(x)) look?
f(g(x)) = f(x^2) = 2(x^2).
What restriction do rational functions have?
Division by 0.
Let f(x) = 2x and g(x) = x^2, how would the expression on the right side of (f+g)(x) look?
(f+g)(x) = 2x + x^2
What’s the notation for subtracting two functions. Let f and g be these two functions.
(f-g)(x).
Let f(x) = 2x, g(x) = x^2, and y = (f○g)(x). What will be the value of y if x = 1?
(f○g)(1) = f(g(1)) = f(1) = 2.
Let f(x) = 2x and g(x) = x^2, how would the expression on the right side of (f/g)(x) look?
(f/g)(x) = 2x/x^2 = 2/x
What’s the notation for dividing two functions. Let f and g be these two functions.
(f/g)(x).
Let f(x) = 3/x-3 and g(x) = 1/x. What’s the domain of f(g(x))?
g(x) cannot be equal to:
0, 1/3
f(x) cannot be equal to:
g(x) = 3
domain (-∞, 0) U (0, 1/3) U (1/3, ∞)
True or false: (f○g)(x) = (g○f)(x).
False.
What’s the notation for adding two functions. Let f and g be these two functions.
(f+g)(x).
What’s a function with an unrestricted domain?
A function that accepts any input that doesn’t violate its inherent rules (division by zero or taking the square root of a negative number).
Let f(x) = 2x, g(x) = x^2, and y = f(g(x)). What’s the value of y if x = 2?
f(g(x)) = f(4) = 8.
What’s a function with a restricted domain? Provide an example.
A function with a restricted domain has specific input values it can take.
E(x)=−2.6x+49x+3994 models the births of Americans, where
𝑥 is the number of years after 2000. The domain is [0,11], representing years from 2000 to 2011.
Let f and g be functions. How is f(g(x)) read?
f of g of x.
What restrictions do radical functions have?
Taking the square root of a negative number.
Let f and g be functions. How is the domain of the composite function f(g(x)) determined?
- If x is not in the domain of g it must be excluded from the domain of f(g(x)).
- If g(x) is not in the domain of f it must be excluded from the domain of f(g(x)).
What’s the domain of two functions combined together via addition, or subtraction, or multiplicaiton, or division? Let these two functions be f and g.
The domain is all the numbers common to both f and g, i.e their intersection is the domain.
What’s a composite function?
A function created by two or more functions. It is also called a nested function.
Let f(x) = 2x and g(x) = x^2, how would the expression on the right side of (f-g)(x) look?
(f-g)(x) = 2x - x^2
Let f and g be functions. If g is nested in f, how would that look in the official notation for composite functions?
(f○g)(x).
What’s the notation for multiplying two functions. Let f and g be these two functions.
(f*g)(x).
Let f(x) = 2x and g(x) = x^2, how would the expression on the right side of (f*g)(x) look?
(f*g)(x) = 2x * x^2 = 2x^3
What’s the domain of a function?
All input values of a function.
Let f and g be functions. How would a composite function of these two functions look like?
f(g(x)).
