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 its domain.

Front

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

Back

The sum of two functions, (f + g)(x), is defined as f(x) + g(x).

Front

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

Back

The product of two functions, (f * g)(x), is defined as f(x) * g(x).

Front

What is the composition of functions, denoted as (g ∘ f)(x)?

Back

The composition of functions is defined as g(f(x)), meaning you apply f first and then g to the result.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x) 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 (f(x)) that the function can produce.

Front

What is the domain restriction for the function (h/g)(x) if g(x) = 0?

Back

The domain restriction is that g(x) cannot equal zero, as division by zero is undefined.

Front

Given f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, find (f + g)(x).

Back

(f + g)(x) = 5x^2 + 6x - 1.

Front

Given f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, find (f - g)(x).

Back

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

Front

What is the formula for finding (gf)(x) if g(x) = 2x + 2 and f(x) = x - 1?

Back

(gf)(x) = g(f(x)) = g(x - 1) = 2(x - 1) + 2 = 2x - 2.