Operations & Compositions & Inverses

Front

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.

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.

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.

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)).

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.

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).

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).

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.