Composition of Functions

Front

Define composition of functions.

Back

The composition of functions is an operation that takes two functions, f and g, and produces a new function, denoted as (f ∘ g)(x) = f(g(x)). It means applying the function g first and then applying the function f to the result.

Front

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

Back

To find f(g(x)), substitute g(x) into f: f(g(x)) = f(2x^2 - 1) = 2(2x^2 - 1) = 4x^2 - 2.

Front

Calculate f(g(3)) if f(x) = 2x and g(x) = 2x^2 - 1.

Back

First, find g(3): g(3) = 2(3^2) - 1 = 17. Then, find f(g(3)): f(17) = 2(17) = 34.

Front

Calculate g(f(-1)) if f(x) = 2x and g(x) = 2x^2 - 1.

Back

First, find f(-1): f(-1) = 2(-1) = -2. Then, find g(-2): g(-2) = 2(-2)^2 - 1 = 7.

Front

What is the result of g(f(x)) if f(x) = 2x and g(x) = 2x^2 - 1?

Back

To find g(f(x)), substitute f(x) into g: g(f(x)) = g(2x) = 2(2x)^2 - 1 = 8x^2 - 1.

Front

Define the term 'function'.

Back

A function is a relation that assigns exactly one output for each input from a set of inputs, known as the domain.

Front

What is the difference between f(g(x)) and g(f(x))?

Back

f(g(x)) means applying g first and then f, while g(f(x)) means applying f first and then g. The order of operations affects the result.

Front

If f(x) = 2x + 3 and g(x) = -3x - 4, find f(g(x)).

Back

f(g(x)) = f(-3x - 4) = 2(-3x - 4) + 3 = -6x - 8 + 3 = -6x - 5.

Front

What is the output of f(g(0)) if f(x) = 2x and g(x) = 2x^2 - 1?

Back

g(0) = 2(0)^2 - 1 = -1. Then, f(g(0)) = f(-1) = 2(-1) = -2.

Front

Explain how to find the inverse of a function.

Back

To find the inverse of a function, swap the input and output variables and solve for the new output variable. The inverse function undoes the action of the original function.