Name________________________________________ Date__________________ Period_________
A11-Square Root Functions & Inverses
Find the inverse of each function. Then give the domain and range of the function and its inverse, restricting the
domain and range when necessary so that the inverse is a function.
1. 𝑓(𝑥) = √4𝑥 + 5
Domain: ____________
2. 𝑓(𝑥) = 2𝑥 2
Range: _____________
Domain: ___________
Range: _____________
Inverse: ______________________________
Inverse: ______________________________
Domain: ___________ Range: ____________
Domain: ___________ Range: ____________
3. 𝑓(𝑥) = √𝑥 − 3
4. 𝑓(𝑥) = 𝑥 2 + 9
Domain: ____________
Range: _____________
Domain: ___________
Range: _____________
Inverse: ______________________________
Inverse: ______________________________
Domain: ___________ Range: ____________
Domain: ___________ Range: ____________
Match each function with its domain and range. Place the corresponding letter in the space provided.
5. _________
𝑓(𝑥) = √𝑥 + 5 − 4
A. 𝑑𝑜𝑚𝑎𝑖𝑛: 𝑥 ≥ −5, 𝑟𝑎𝑛𝑔𝑒: 𝑓(𝑥) ≥ 4
6. _________
𝑓(𝑥) = √𝑥 − 5 + 4
B. 𝑑𝑜𝑚𝑎𝑖𝑛: 𝑥 ≥ −5, 𝑟𝑎𝑛𝑔𝑒: 𝑓(𝑥) ≥ −4
7. _________
𝑓(𝑥) = √𝑥 + 5 + 4
C. 𝑑𝑜𝑚𝑎𝑖𝑛: 𝑥 ≥ 5, 𝑟𝑎𝑛𝑔𝑒: 𝑓(𝑥) ≥ 4
Graph the function and its inverse. Is the inverse a function?
8. 𝑓(𝑥) = √𝑥 + 2
9. 𝑓(𝑥) = 𝑥 2 − 1
10. 𝑓(𝑥) = √𝑥 + 3
11. 𝑓(𝑥) = (7 − 𝑥)2
Use composition to show that f and g are inverses.
12. 𝑓(𝑥) = (𝑥 − 4)2 𝑎𝑛𝑑 𝑔(𝑥) = √𝑥 + 4
𝑥
13. 𝑓(𝑥) = 5𝑥 2 , 𝑥 > 0 𝑎𝑛𝑑 𝑔(𝑥) = √5
Use the following situations for Questions 14 & 15.
The formula for an object that is thrown downward from a height of 25 feet is 𝑑 = 25 + 15𝑡 2 , where d is the
distance the object travels (in feet) and t is the time it takes (in seconds).
14. Find the inverse of the formula. Is the inverse a function?
15. Use the inverse to find the distance that corresponds to a time of 30 seconds. Round your answer to the
nearest hundredth.
Write a square root function with the following intercepts.
16. 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡: −4
17. 𝑥 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡: 8
Determine whether each statement is always, sometimes, or never true.
18. A square root function has both x- and y-intercepts.
19. The range of a square root function includes positive and negative real numbers.
20. A square root function has two y-intercepts.
21. For any real number a, the domain of 𝑓(𝑥) = √𝑥 − 𝑎 includes positive numbers.
Graph each function. Give the x- and y-intercepts.
22. 𝑓(𝑥) = √𝑥 + 2
x-intercept: __________________
y-intercept: __________________
23. 𝑓(𝑥) = √𝑥 − 6 + 2
x-intercept: __________________
y-intercept: __________________
24. 𝑓(𝑥) = 3 + √𝑥 + 4
x-intercept: __________________
y-intercept: __________________
25. 𝑓(𝑥) = √𝑥 + 5 − 2
x-intercept: __________________
y-intercept: __________________