Exploring Functions and Their Inverses

Exploring Functions and Their Inverses

Assessment

Flashcard

Mathematics

12th Grade

Practice Problem

Hard

Created by

Wayground Content

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

2.

FLASHCARD QUESTION

Front

What is the composition of functions?

Back

The composition of functions, denoted as (f ∘ g)(x), is the application of one function to the results of another. It is defined as f(g(x)).

3.

FLASHCARD QUESTION

Front

Find the composition (f ∘ g)(x) if f(x) = x^2 and g(x) = x + 1.

Back

(x + 1)^2.

4.

FLASHCARD QUESTION

Front

What is the range of the function f(x) = |x|?

Back

[0, ∞).

5.

FLASHCARD QUESTION

Front

What is the inverse of a function?

Back

The inverse of a function f(x) is a function that reverses the effect of f, denoted as f^{-1}(x). If f(a) = b, then f^{-1}(b) = a.

6.

FLASHCARD QUESTION

Front

How do you find the inverse of a quadratic function?

Back

To find the inverse of a quadratic function, complete the square and solve for x in terms of y.

7.

FLASHCARD QUESTION

Front

Find the inverse of the function f(x) = x^2 + 8x + 16 using completing the square.

Back

f^{-1}(x) = √x - 4.

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