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
PolarNik [594]
2 years ago
5

Exercise 3.5. For each of the following functions determine the inverse image of T = {x ∈ R : 0 ≤ [x^2 − 25}.

Mathematics
1 answer:
masya89 [10]2 years ago
5 0

a. The inverse image of f(x) is f⁻¹(x) = ∛(x/3)

b. The inverse image of g(x) is g^{-1}(x) = e^{x}

c. The inverse image of <u>h</u>(x) is h⁻¹(x) = x + 9

<h3 /><h3>The domain of T</h3>

Since T = {x ∈ R : 0 ≤ [x^2 − 25} ⇒ x² - 25 ≥ 0

⇒ x² ≥ 25

⇒ x ≥ ±5

⇒ -5 ≤ x ≤ 5.

<h3>Inverse image of f(x)</h3>

The inverse image of f(x) is f⁻¹(x) = ∛(x/3)

f : R → R defined by f(x) = 3x³

Let f(x) = y.

So, y = 3x³

Dividing through by 3, we have

y/3 = x³

Taking cube root of both sides, we have

x = ∛(y/3)

Replacing y with x we have

y = ∛(x/3)

Replacing y with f⁻¹(x), we have

So,  the inverse image of f(x) is f⁻¹(x) = ∛(x/3)

<h3>Inverse image of g(x)</h3>

The inverse image of g(x) is g^{-1}(x) = e^{x}

g : R+ → R defined by g(x) = ln(x).

Let g(x) = y

y =  ln(x)

Taking exponents of both sides, we have

e^{y} = e^{lnx} \\e^{y} = x

Replacing x with y, we have

y = e^{x}

Replacing y with g⁻¹(x), we have

So, the inverse image of g(x) is g^{-1}(x) = e^{x}

<h3>Inverse image of h(x)</h3>

The inverse image of <u>h</u>(x) is h⁻¹(x) = x + 9

h : R → R defined by h(x) = x − 9

Let y = h(x)

y = x - 9

Adding 9 to both sides, we have

y + 9 = x

Replacing x with y, we have

x + 9 = y

Replacing y with h⁻¹(x), we have

So, the inverse image of <u>h</u>(x) is h⁻¹(x) = x + 9

Learn more about inverse image of a function here:

brainly.com/question/9028678

You might be interested in
The screen on Lin's cell phone allows for 8 lins of text per message. The maximum number of characters for each message is 10. H
julia-pushkina [17]
There will 80 characters per each line hold. Hope it help!
8 0
3 years ago
120% of a number is 45 find the number
Bezzdna [24]
Hello,

Here is your answer:

The proper answer to this question is "37.5".

Your answer is 37.5!

If you need anymore help feel free to ask me!

Hope this helps!
3 0
3 years ago
The temperature at 6pm was 0 degrees Fahrenheit at 10 pm the temperature was -11.2 degrees Fahrenheit write an expression that y
lana66690 [7]
The answer is the temperature goes down 2.8° every hour and the expression is x=-11.2/4 because 4 is how many hours between 6pm and 10pm and its -11.2 because that was how much the temperature dropped from 6pm to 10pm
8 0
3 years ago
11/12 + -7/12 simpilist form
Vaselesa [24]

11/12 - 7/12 = 4/12 = 1/3

please give brainliest

7 0
2 years ago
Read 2 more answers
In which town does the total number have meaning
olganol [36]
This question is incomplete, please provide more information!
5 0
2 years ago
Other questions:
  • If s(x) = x – 7 and t(x) = 4x2 – x + 3, which expression is equivalent to (t*s)(x)
    12·1 answer
  • A recent physical inventory at a department store reports a merchandise value of $875,435. The merchandise book value was $907,3
    7·1 answer
  • what is the similarity ratio of the smaller to the larger similar cylinders? enter your answer as a:b​
    5·1 answer
  • After dinner, your aunt serves slices of apple pie. Would you rather have a slice with a central angle equal to
    9·2 answers
  • What can I multiply 4/3 by to make it 1⅓​, jk what's up
    10·1 answer
  • How does the length of the hypotenuse in a right triangle relate to the lengths of the legs?
    10·1 answer
  • The amount c in grams of a 100 gram sample of carbon-14 remaining after t years is represented by the equation c= 100 (0.99988)t
    15·1 answer
  • Who ever answers this I will mark as brainliest
    7·1 answer
  • Choose the graph that matches the following system of equations:
    6·2 answers
  • Nadia is a stockbroker. She earns 12% commission each week. Last week, she sold $5400 worth of stocks. How much did she make las
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!