Algebra 2 worksheet inverses of functions more domain and range

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Lesson Worksheet: Inverse of a Function Mathematics • Class XII

In this worksheet, we will practice finding the inverse of a function by changing the subject of the formula.

Q1:

The following tables are partially filled for functions 𝑓 and 𝑔 that are inverses of each other. Determine the values of 𝑎, 𝑏, 𝑐 , 𝑑, and 𝑒.

• A𝑎=−26, 𝑏=3, 𝑐 =4, 𝑑=5, 𝑒=14
• B𝑎=2, 𝑏=−19 , 𝑐=4, 𝑑=5, 𝑒=14
• C𝑎=2, 𝑏=−19, 𝑐=4, 𝑑=1, 𝑒 =6
• D𝑎=−26, 𝑏=−19, 𝑐=4, 𝑑=1, 𝑒=14
• E𝑎=−26, 𝑏=3 , 𝑐=4, 𝑑=1, 𝑒=6

Q2:

Does the function 𝑓, where 𝑓={(5,3),(9,7),(1 1,10)}, have an inverse?

• AYes
• BNo

Q3:

The figure below represents the function 𝑓𝑋→𝑌:. Find the value of 𝑓(4).

• A10
• B13
• C8
• D4

Q4:

Using the graph of 𝑔(𝑥), find 𝑔(2).

Q5:

Which of the following functions does not have an inverse over its whole domain? Assume that the codomain of each function is equal to its range.

• A𝑓(𝑥)=2
• B𝑓(𝑥)=𝑥
• C𝑓(𝑥)=2𝑥
• D𝑓(𝑥)=1𝑥

Q6:

Find 𝑓(𝑥)  for 𝑓(𝑥 )=12𝑥+3.

• A𝑓(𝑥)=−2𝑥+6
• B𝑓(𝑥)=−12𝑥−3
• C𝑓(𝑥)=𝑥−3
• D𝑓(𝑥)=2𝑥−6

Q7:

Find 𝑓(𝑥) for 𝑓(𝑥)=√𝑥+3 and state the domain.

• A𝑓(𝑥)=(−𝑥−3)  for 𝑥≥−3
• B𝑓(𝑥)=−(𝑥−3) for 𝑥≥3
• C𝑓(𝑥)=(𝑥−3) for 𝑥≥3
• D𝑓(𝑥)=(𝑥−2) for 𝑥≥2

Q8:

Find 𝑓(𝑥) for 𝑓(𝑥)=3 +√𝑥.

• A𝑓(𝑥)=𝑥−3
• B𝑓(𝑥)=(𝑥−3) 
• C𝑓(𝑥)=−(𝑥−3)
• D𝑓(𝑥)=−3−√𝑥 

Q9:

Find 𝑓(𝑥) for 𝑓(𝑥)=(𝑥−2)−3, where 𝑥≥2, and state the domain.

• A𝑓(𝑥)=√𝑥+3+2 for 𝑥≥−3
• B𝑓(𝑥)=√𝑥−3+2 for 𝑥≥3
• C𝑓(𝑥)=−√𝑥+3−2 for 𝑥≥−3
• D𝑓(𝑥)=√𝑥+3−2  for 𝑥≥−3

Q10:

The solid part of the following graph of 𝑓(𝑥)=(𝑥−3) shows how we can restrict the domain to obtain an inverse.

What is the domain of the inverse?

• A𝑥>0
• B𝑥 ≤0
• C𝑥≥0
• D𝑥≥3
• E𝑥<3

What is the range of the inverse?

• A𝑥<3
• B𝑥>3
• C𝑥 ≥0
• D𝑥≤3
• E𝑥≤3

Give a formula for the inverse.

• A𝑓(𝑥)=−3−√𝑥 
• B𝑓(𝑥)=3+√𝑥
• C𝑓(𝑥)=3−3√𝑥 
• D𝑓(𝑥) =3−√𝑥
• E𝑓(𝑥)=−3+√𝑥

This lesson includes 70 additional questions and 282 additional question variations for subscribers.