Functions | Summary and Q&A

TL;DR

This content provides solutions to algebraic function problems, including calculating values, finding inverse functions, determining domains, and identifying one-to-one functions.

Key Insights

• 📔 The content covers various algebraic function problems, such as calculating values, finding inverses, and determining domains.
• 🫥 Functions that pass the vertical line test are considered functions, while those that fail are not.
• ❣️ Inverse functions are found by switching x and y and solving for y.
• 🗂️ The domain of a function divided by another function excludes values that make the denominator zero.
• 🫥 One-to-one functions pass the horizontal line test, with each horizontal line intersecting the function at most once.
• 🥺 Careful consideration is required when factoring trinomials with leading coefficients not equal to one.
• 🆘 Substituting specific values into functions can help determine their outputs.

Transcript

number one calculate the value of f of two using the function shown below so all we need to do is replace x with two so we have two to the third plus five times two squared minus nine two times two times two is eight two squared or two times two is four and five times four is twenty twenty minus 9 is 11 8 plus 11 is 19. so therefore answer choice e... Read More

Questions & Answers

Q: How do you calculate the value of f(2) using the given function?

To calculate the value of f(2), substitute x with 2 in the function and simplify.

Q: How do you find the inverse function of a given function?

To find the inverse function, replace f(x) with y, switch x and y, and solve for y.

Q: What is the value of x when f(x) equals -15?

Substitute f(x) with -15, rearrange the equation, factorize, and solve for x.

Q: How do you determine if two functions are inverses of each other?

To prove that f(x) and g(x) are inverses, show that f(g(x)) and g(f(x)) both equal x.

Q: Which functions pass the vertical line test?

Functions that pass the vertical line test have only one point of intersection with any vertical line.

Q: Which function is not a one-to-one function?

The function that fails the horizontal line test, meaning it intersects a horizontal line at more than one point, is not a one-to-one function.

Q: How do you find the value of y in the function f(4, y) = 48?

Substitute x with 4 in the function, simplify the equation, and solve for y.

Q: What is the domain of f divided by g?

The domain of f divided by g is all real numbers except the values that make the denominator equal to zero.

Summary & Key Takeaways

• Calculation: Calculate the value of f(2) using the given function f(x).

• Inverse Function: Find the inverse function of the given function f(x).

• Value of x: Determine the value of x when f(x) equals -15.