5.5 Review

Front

What is the composition of functions?

Back

The composition of functions is a way to combine two functions, denoted as (g∘f)(x) = g(f(x)). It means you apply the function f first and then apply the function g to the result.

Front

If f(x) = 2x - 8 and g(x) = 4x, what is g(f(x))?

Back

g(f(x)) = g(2x - 8) = 4(2x - 8) = 8x - 32.

Front

What does the notation (f + g)(x) represent?

Back

The notation (f + g)(x) represents the sum of two functions, defined as (f + g)(x) = f(x) + g(x).

Front

If f(x) = x^2 + 25 and g(x) = x - 5, what is (f + g)(x)?

Back

(f + g)(x) = (x^2 + 25) + (x - 5) = x^2 + x + 20.

Front

What is the difference of functions?

Back

The difference of functions is denoted as (f - g)(x) = f(x) - g(x). It represents the subtraction of one function from another.

Front

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

Back

g(f(-2)) = g(2) = 3(2) + 1 = 7.

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 for a function to be linear?

Back

A function is linear if it can be expressed in the form f(x) = mx + b, where m and b are constants.

Front

What is the significance of 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.