Understanding Functions and Their Inverses

The video tutorial explains how to solve for x using given equations involving a function and its inverse. It starts by simplifying the equation to isolate the inverse function, then explores the relationship between a function and its inverse. Finally, it uses this understanding to solve for x, demonstrating that x equals 13.

What are the two pieces of information given in the problem?

• 11 equals eight plus f inverse of x minus three, and f of two equals 10

• 11 equals eight plus f inverse of x minus three, and f of three equals 5

• 11 equals eight plus f of x minus three, and f of three equals 10

• 11 equals eight plus f inverse of x minus three, and f of three equals 10

What is the first step in simplifying the equation?

• Divide both sides by eight

• Multiply both sides by eight

• Subtract eight from both sides

• Add eight to both sides

What is the purpose of subtracting eight from both sides of the equation?

• To eliminate the inverse function

• To find the value of x

• To simplify the function

• To isolate the inverse function

What does the function f do according to the given information?

• Maps from 10 in the range to 3 in the domain

• Maps from 3 in the range to 10 in the domain

• Maps from 3 in the domain to 10 in the range

• Maps from 10 in the domain to 3 in the range

What does the inverse function f inverse do?

• Maps from 10 in the range to 3 in the domain

• Maps from 10 in the domain to 3 in the range

• Maps from 3 in the range to 10 in the domain

• Maps from 3 in the domain to 10 in the range

What does the equation f inverse of x minus three equals three imply?

• x minus three equals 10

• x plus three equals 3

• x plus three equals 10

• x minus three equals 3

How does the inverse function relate to the original function?

• It doubles the mapping of the original function

• It reverses the mapping of the original function

• It halves the mapping of the original function

• It squares the mapping of the original function

What equation do we get after applying the inverse function concept?

• x plus three equals 13

• x minus three equals 10

• x minus three equals 13

• x plus three equals 10

What is the value of x after solving the equation?

• x equals 10

• x equals 13

• x equals 3

• x equals 8

What is the final step to find the value of x?

• Subtract three from both sides

• Add three to both sides

• Divide both sides by three

• Multiply both sides by three