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
Nady [450]
3 years ago
15

Consider the function h(x) =x2 – 12x + 58.

Mathematics
1 answer:
alekssr [168]3 years ago
7 0

Answer:

The correct option is;

x ≥ 6; h⁻¹(x) = 6 +√(x - 22)

Step-by-step explanation:

Given the function, h(x) = x² - 12·x + 58

We can write, for simplification;

y = x² - 12·x + 58

Therefore;

When we put x as y to find the inverse in terms of x, we get;

x = y² - 12·y + 58

Which gives;

x - x = y² - 12·y + 58 - x

0 = y² - 12·y + (58 - x)

Solving the above equation with the quadratic formula, we get;

0 = y² - 12·y + (58 - x)

x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}

a = 1, b = -12, c = 58 - x

Therefore;

x = \dfrac{-(-12)\pm \sqrt{(-12)^{2}-4\times (1)\times (58 - x)}}{2\times (1)}= \dfrac{12\pm \sqrt{144-232 + 4 \times x)}}{2}

x =  \dfrac{12\pm \sqrt{4 \times x - 88}}{2} =  \dfrac{12\pm \sqrt{4 \times (x - 22)}}{2}  = \dfrac{12\pm 2 \times \sqrt{ (x - 22)}}{2}

x = \dfrac{12\pm 2 \times \sqrt{ (x - 22)}}{2} = {6 \pm  \sqrt{ (x - 22)}}

We note that for the function, h(x) = x² - 12·x + 58, has no real roots and the real minimum value of y is at x = 6, where y = 22 by differentiation as follows;

At minimum, h'(x) = 0 = 2·x - 12

x = 12/2 = 6

Therefore;

h(6) = 6² - 12×6 + 58 = 22

Which gives the coordinate of the minimum point as (6, 22) whereby the minimum value of y = 22 which gives √(x - 22) is always increasing

Therefore, for x ≥ 6, y or h⁻¹(x) = 6 +√(x - 22)  and not 6 -√(x - 22) because 6 -√(x - 22) is less than 6

The correct option is  x ≥ 6; h⁻¹(x) = 6 +√(x - 22).

You might be interested in
2 mi, 1.5 mi, 2.5 mi​
Vaselesa [24]

what is the question

8 0
3 years ago
Read 2 more answers
Solve the system of equations by elimination.<br> -X + y = -13 <br>-8x - 4y = -8​
Ksivusya [100]
The first one is -2x+15y=-13
The second one is uhhh well I d and K
3 0
3 years ago
Read 2 more answers
Packaging milk in cardboard containers is a way to prevent destruction of which vitamin by ultraviolet light?
Diano4ka-milaya [45]
I had to look for the options and here is my answer:
The reason why cardboard containers are being used when packaging milk is to prevent destroying THIAMIN by the ultraviolet light from the sun. Thiamine is known as Vitamin B1. Hope this helps.
5 0
3 years ago
Cuantas botellas de 3/4 de litro se pueden llenar con una garrafa de 300 litros?
Airida [17]
The question in English
<span>How many bottles of 3/4 liter if you can fill with a 300-liter bottle?

step 1
divide 300 liters by 3/4 liter
so
300/(3/4)----> 300*(4/3)----> 300*4/3---> 1200/3----> 400 bottles

the answer is
400 bottles

the answer in Spanish

</span>Paso 1
divida 300 litros entre 3/4 litro
de esta manera
300/(3/4)----> 300*(4/3)----> 300*4/3---> 1200/3----> 400 botellas

La respuesta es
400 botellas
6 0
3 years ago
Please help what is the answer a b c or d
bonufazy [111]

Answer:

A

Step-by-step explanation:

I did test rf

4 0
2 years ago
Other questions:
  • You are asked to bake muffins for a breakfast meeting. Just as you are about to start making them, you get a call saying that th
    10·1 answer
  • Write an equation in point-slope form for the line that has a slope of 5/6 and contains the point (−8, −4) Help ASAP!!
    11·1 answer
  • Could you please help me......
    9·1 answer
  • A tree grows three feet per year. What happens to the growth of the tree when the number of years changes
    8·2 answers
  • Which satisfies the given inequality 6x &lt; 24<br> a. 10 <br> b. 8<br> c. 6<br> d. 2
    10·1 answer
  • How do you solve <br> 8.4-6.8=-3.2y+16.4
    7·2 answers
  • 128 less than a number is 452
    9·2 answers
  • The measures of the angles of a triangle are shown in the figure below. Solve for x.
    14·2 answers
  • 8. If ADGH - ADEF, find the value of x.<br> Help ASAP please
    9·2 answers
  • A bag of 20 counters
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!