# Math

The function f(x)=(x-5)^2+2 is not one-to-one. Identify a restricted domain that makes the function one-to-one, and find the inverse function.

a. restricted domain: x>or=5; f^-1(x)=5-sqrt(x-2)

b. restricted domain: x>or=5; f^-1(x)=5+sqrt(x-2)

c. restricted domain: x<or=5; f^-1(x)=5+sqrt(x+2)

d. restricted domain: x<or=-5; f^-1(x)=5+sqrt(x-2)

I really need help if someone could please explain this to me, I would greatly appreciate it. Thank you!

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
1. the axis of symmetry is the line x=5
So, any domain on one side of that line will be one-to-one.

Now, for the inverse, swap variables and solve for f^-1

x = (f-5)^2+2
x-2 = (f-5)^2
f-5 = ±√(x-2)
f = 5±√(x-2)

Now, we need one branch only, but √(x-2) is only defined for x>=2

On the original parabola, the right branch is x>=5. So, only A or B is a candidate, and so B is the choice.

1. 👍
2. 👎
3. ℹ️
4. 🚩
2. 🦄make sure to use starcode: ⭐iamsanna⭐ when buying Robux in Roblox🦄 Thank you for reading this!!

-notiamsanna

1. 👍
2. 👎
3. ℹ️
4. 🚩

## Similar Questions

1. ### math

graph the function and identify the domain and range y=-3x^2

2. ### Algebra

graph the function and identify the domain and range y=-4x^2

3. ### Algebra plz help

1.Identify the domain and range of the following relation. {(3,7),(3,8),(3,-2),(3,4),(3,1)} A.Domain:{3} Range:{-2,1,4,7,8}**** B.Domain:{-2,1,4,7,8} Range:{3} C.Domain:{all real numbers} Range:{all real numbers} D.Domain:O/

4. ### Algebra

1.Identify the domain and range of the following relation. {(3,7),(3,8),(3,-2),(3,4),(3,1)} A.Domain:{3} Range:{-2,1,4,7,8}**** B.Domain:{-2,1,4,7,8} Range:{3} C.Domain:{all real numbers} Range:{all real numbers} D.Domain:O/

1. ### Math

compare the parent function f(x)=x^2 to the quadractic function f(x)=-2x^2-6. the 6 in the function does which of the following? a.it makes the graph narrower than the parent function. b.it makes the graph wider than the parent

2. ### calcius

Determine whether the relation represents a function. If it is a function, state the domain and range. {(-2, 1), (-1, -2), (0, -3), (1, -2), (3, 6)} a. function domain: {-2, -1, 0, 1, 3} range: {1, -2, -3, 6} b. function domain:

3. ### Algebra Check

What is the domain of the function below? ((0,2),(3,1) (5,2) (8,4)) a. (1,2,4) b. (0,3,5,8)** c. (0,1,2,3,4,5,8) d. ((0,2),(3,1) (5,2) (8,4)) Is the following relation a function? ((0.3,0.6), (0.4,0.8), (0.3,0.7), (0.5,0.5)) a.

4. ### Algebra 2

The graph of an absolute value function opens up and has a vertex of (0, -3). The domain of the function is . The range of the function is

1. ### Algebra

Find the domain of each square root function. Then use the domain to match the radical function with it’s graph. The graphs are labeled (a) through (f) and are shown in [-10,10,1] by [-10,10,1] viewing rectangles. f(x)=~(8-2x)

2. ### Precalculus

The function f has a domain of [0,5]and a range of [0,3]. Start by sketching a potential graph of f. Suppose the function k is defined as k(x)=f(x−3). Determine the domain and range of k. Domain: Range:

3. ### math

5.6.8 - Quick Check: Formalizing Relations and Functions What is the domain of the function below? {(0, 2), (3, 1), (5, 2), (8, 4)}? {1, 2, 4} {0, 3, 5, 8} ✅ {0, 1, 2, 3, 4, 5, 8} {(0, 2), (3, 1), (5, 2), (8, 4)} Is the