1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
madam [21]
3 years ago
12

The function ƒ(x) = (x − 1)^2 + 5 is not one-to-one. Find a portion of the domain where the function is one-to-one and find an i

nverse function.
The restricted domain for ƒ is ?
Mathematics
1 answer:
melisa1 [442]3 years ago
3 0

Answer:

f(x)=(x-1)^2+5 with domain x>1 and range y>5 has inverse g(x)=sqrt(x-5)+1 with domain x>5 and range y>1.

Step-by-step explanation:

The function is a parabola when graphed. It is in vertex form f(x)=a(x-h)^2+k where (h,k) is vertex and a tells us if it's reflected or not or if it's stretched. The thing we need to notice is the vertex because if we cut the graph with a vertical line here the curve will be one to one. So the vertex is (1,5). Let's restrict the domain so x >1.

* if x>1, then x-1>0.

* Also since the parabola opens up, then y>5.

So let's solve y=(x-1)^2+5 for x.

Subtract 5 on both sides:

y-5=(x-1)^2

Take square root of both sides:

Plus/minus sqrt(y-5)=x-1

We want x-1>0:

Sqrt(y-5)=x-1

Add 1 on both sides:

Sqrt(y-5)+1=x

Swap x and y:

Sqrt(x-5)+1=y

x>5

y>1

You might be interested in
20 minus the product of 3 and 5.
olganol [36]

Answer:

5

Step-by-step explanation:

6 0
3 years ago
Adam will plant up to 41 acres on his farm with wheat and corn. Fewer than 28 acres will be planted with corn.
Eddi Din [679]
Both A and D are correct. Yup.
8 0
3 years ago
Read 2 more answers
What is the solution to the inequality? -3x < 24 
Paraphin [41]

Answer:

x > -8

Step-by-step explanation:

Divide both sides by -3 to get x by itself. Dividing by a negative number will switch the less-than symbol to a greater-than symbol. -3x ÷ -3 = x and 24 ÷ -3 = -8. When you put it all together, you get x > -8

8 0
3 years ago
Please help me with this
umka21 [38]

Answer:

Mixed Number : 2 \frac{2}{3}

Improper Fraction : \frac{8}{3}

Step-by-step explanation:

5 0
3 years ago
When 12 is divided by which statement about the quotient is true?<br> A
Novay_Z [31]

Answer:

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • Y=f(x)=(1/6)^x find f(x) when x=1/4
    11·2 answers
  • How do I solve this problem
    6·1 answer
  • On a town map, each unit of the coordinate plane represents 1 mile. Three branches of a bank are located at A(−3, 1), B(1, 4), a
    11·1 answer
  • Which of the lines graphed has a slope of 3 and a y-intercept of 2?​
    8·2 answers
  • In the following figure, EM is tangent to circle A at point C.
    14·1 answer
  • Two students, Carlos and Sophie, factored the trinomial -4x2 − 10x + 6. Sophie factored it as -2(2x − 1)(x + 3) and Carlos facto
    6·1 answer
  • Find the domain of the rational function 9x/(x+5)(x+3)
    15·1 answer
  • Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? Check all that apply. For any value of x, g(x) will alway
    14·1 answer
  • I need help I dont understand this​
    6·1 answer
  • Please help I don’t know what to do
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!