composition of functions+function operations

Front

What is a function composition?

Back

Function composition is the process of applying one function to the results of another function. If you have two functions, f(x) and g(x), the composition is denoted as (f ∘ g)(x) = f(g(x)).

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

f(g(3)) = f(17) = 34.

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

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

Tags

CCSS.HSF-BF.A.1C

Front

What is the notation for function composition?

Back

The notation for function composition is (f ∘ g)(x), which means f(g(x)).

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

(f ∘ g)(-1) = f(g(-1)) = f(1) = 1.

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

f(g(x)) = f(2x^2 - 1) = 4x^2 - 2.

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

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

Tags

CCSS.HSF-BF.A.1C

Front

What is 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.

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function has the form f(x) = mx + b, while a quadratic function has the form f(x) = ax^2 + bx + c.