# 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. 👍 0
2. 👎 0
3. 👁 612
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. 👍 0
2. 👎 0
2. 🦄make sure to use starcode: ⭐iamsanna⭐ when buying Robux in Roblox🦄 Thank you for reading this!!

-notiamsanna

1. 👍 0
2. 👎 1

## Similar Questions

1. ### 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/

2. ### 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/

Did I get these practice questions right? 1. Suppose that f is an even function whose domain is the set of all real numbers. Then which of the following can we claim to be true? ***The function f has an inverse f –1 that is

The domain of f(x)=(1)/(sqrt(x^2-6x-7)) is (1, 7) [-1, 7] x > -1 or x < 7 ***{x < -1}U{x > 7} (-∞, -1]U[7, ∞) 2. In which of the following is y a function of x? I. y^2=9-x^2 II. |y|=x III. y=(sqrt(x^2))^3 I only II only III

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. ### 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.

3. ### 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

4. ### math

A movie theater seats 500 people. For any particular show, the amount of money the theater makes is a function m(n) of the number of people, n, in attendance. If a ticket costs 2 dollars, find the domain and range of this

1. ### Gr.11 - Rational functions graphing.

1. Identify a rational function whose graph is a horizontal line except for two holes. Graph the function. 2. Identify a rational function who graph lies entirely above the x-axis and has a single vertical asymptote. Graph the

2. ### math

An increasing linear function with independent variable x and dependent variable y approaches the point (−1, 1). If this function is defined only when x is greater than −1 and y is greater than 1, what are the domain and range

3. ### algebra

Identify the maximum or minimum value and the domain and range of the graph of the function y=2(x-3)^2-4 Can someone please help me.

4. ### Calculus

Explain, using the theorems, why the function is continuous at every number in its domain. F(x)= 2x^2-x-3 / x^2 +9 A) F(x) is a polynomial, so it is continuous at every number in its domain. B) F(x) is a rational function, so it