(Q7.) Sample 3 GCC Math 101/120 Common Final Intermediate Algebra

TL;DR

This content explains how to find the equation for the inverse function of a given equation through four steps.

Transcript

for question number seven we have the function f of x is equal to four x plus three over five x minus one and our goal is to find an equation for its inverse so here are four steps step one let me write this outside first step one whenever you see f of x and you want to find the equation for the inverse let's write f of x as y so i see f of x i wil... Read More

Key Insights

• 😀 When finding the equation for the inverse function, the first step is to replace "f(x)" with "y" in the given equation.
• ❣️ Switching "x" and "y" in the equation is a critical step in finding the inverse function.
• 💛 Isolating the new "y" variable often involves multiplying both sides of the equation by the lowest common denominator.

Questions & Answers

Q: What are the four steps to find the equation for the inverse function?

The four steps are: 1) Replace "f(x)" with "y", 2) Switch "x" with "y" and rewrite the equation, 3) Isolate the new "y" by multiplying both sides by the lowest common denominator, and 4) The isolated "y" is the equation for the inverse function.

Q: Why is multiplying both sides by the lowest common denominator necessary in step 3?

Multiplying both sides by the lowest common denominator helps eliminate the fractions in the equation, simplifying the process of isolating the new "y" variable.

Q: What is the significance of switching "x" and "y" in step 2?

Switching "x" and "y" allows us to interchange the roles of the independent and dependent variables, which is crucial in finding the equation for the inverse function.

Q: How do you represent the inverse function in notation?

The inverse function is represented using the notation f inverse, denoted as f^-1(x). In this case, the inverse function is equal to (x + 3) / (5x - 4).

Summary & Key Takeaways

• Step 1: Replace "f(x)" with "y" in the given equation.

• Step 2: Switch "x" with "y" and rewrite the equation.

• Step 3: Isolate the new "y" by multiplying both sides by the lowest common denominator.

• Step 4: The isolated "y" is the equation for the inverse function.