2.2 Operations with Functions

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input from a given set.

Front

What does it mean to add two functions, f(x) and g(x)?

Back

(f + g)(x) = f(x) + g(x) for all x in the domain of f and g.

Front

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

Back

(f - g)(x) = f(x) - g(x) for all x in the domain of f and g.

Front

What is the formula for multiplying two functions, f(x) and g(x)?

Back

(f * g)(x) = f(x) * g(x) for all x in the domain of f and g.

Front

How do you divide two functions, f(x) and g(x)?

Back

(f / g)(x) = f(x) / g(x) for all x in the domain of f and g, where g(x) ≠ 0.

Front

What is the composition of functions, f(x) and g(x)?

Back

(f ∘ g)(x) = f(g(x)) for all x in the domain of g.

Front

If f(x) = 2x and g(x) = 2x - 7, what is (f/g)(x)?

Back

(f/g)(x) = (2x)/(2x - 7).

Front

Given f(x) = x^2 + 5 and g(x) = 2x^3 - 1, how do you find (f/g)(-3)?

Back

(f/g)(-3) = -14/55.

Front

What is the result of (g + f)(x) if g(x) = 4x - 4 and f(x) = 5x + 4?

Back

(g + f)(x) = 9x.

Front

How do you calculate (f - g)(n) for f(x) = 5x + 4 and g(x) = 4x - 4?

Back

(f - g)(n) = n + 8.