Operations & Compositions & Inverses

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What are inverse functions?

Back

Inverse functions are functions that reverse the effect of the original function. If f(x) takes an input x and produces an output y, then the inverse function f⁻¹(y) takes y and produces the original input x.

Tags

CCSS.HSF-BF.B.4A

Front

How can you determine if two functions are inverses of each other?

Back

Two functions f(x) and g(x) are inverses if f(g(x)) = x and g(f(x)) = x for all x in the domain of both functions.

Tags

CCSS.HSF-BF.B.4B

Front

What is the significance of the line y = x in relation to inverse functions?

Back

The line y = x is the line of reflection for inverse functions. The graph of a function and its inverse are symmetric with respect to this line.

Tags

CCSS.HSF-BF.B.4C

Front

What is function composition?

Back

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

Tags

CCSS.HSF-BF.A.1C

Front

Given p(x) = 3x + 4 and q(x) = 2x², how do you find p(q(x))?

Back

To find p(q(x)), substitute q(x) into p(x): p(q(x)) = p(2x²) = 3(2x²) + 4 = 6x² + 4.

Tags

CCSS.HSF-BF.A.1C

Front

What is the formula for the sum of two functions f(x) and g(x)?

Back

The sum of two functions is given by (f + g)(x) = f(x) + g(x).

Tags

CCSS.HSF-BF.A.1B

Front

How do you find the value of f(g(a))?

Back

To find f(g(a)), first evaluate g(a) to get a value, then substitute that value into f(x).

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 a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants.