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
VladimirAG [237]
3 years ago
15

What are the domain and range of the logarithmic function f(x) = log7x? Use the inverse function to justify your answers.

Mathematics
2 answers:
kolezko [41]3 years ago
5 0
The domain  is  x > 0  or (0,∞)

the range is  f(x) >= 0

the inverse of the function is  f-1(x)= (10^x ) / 7 

here we see that domain is >= 0  which is the range of f(x) and the range is > 0 whch equals the domain of f(x)

    
snow_tiger [21]3 years ago
3 0

We have been given the function

f(x)=\log 7x

Domain is the set of x values for which the function is defined. We know that a logarithm function is defined for all values greater than zero.

Thus, for the domain , we have

7x>0\\x>0

The domain is given by \left \{ x \in R, x>0 \right \}

The range is the set of y values for which the function is defined. For this logarithm function, we can take any values. Hence, the range of the function is all real number.

Now let us find the inverse of the function.

y=\log (7x)\\ \text{Swap x and y, we get}\\ x=log(7y)\\ \text{Now, we find the value of y}\\  7y=10^x\\ y=\frac{1}{7}10^x\\ f^{-1}(x)=\frac{1}{7}10^x

The domain of the inverse function is all real number and range is all values greater than zero.

We know that the domain of the function is range of the inverse function and the range of the function is domain of the inverse function.

Therefore, it justifies our solution.

You might be interested in
Type the solution.y=–3x–7y=x–3
Andrej [43]

Answer:

(x,y)=(-1,-4)

Step-by-step explanation:

y=–3x–7

y=x–3

(y=)-3x-7=x-3

-3x-x=-3+7

-4x=4

x=4/(-4)

x=-1

y=x-3

y=-1-3

y=-4

(x,y)=(-1,-4)

6 0
2 years ago
34 &lt; 5x + 9 &lt; 44<br> Inequality
Ksivusya [100]

Answer:

5 < x < 7

Step-by-step explanation:

- Move all terms not containing  x  from the center section of the inequality.

25  <  5 x  <  35

- Divide each term in the inequality by  5 .

5 < 1x < 7

5 < x < 7

i hope this helps :)

5 0
2 years ago
One leg of a right isosceles Triangle is 6ft what is The area of The Triangle
AVprozaik [17]

Answer:

18ftx^{2}

Step-by-step explanation:

so fine area you do side x side and divide by two

6 x 6= 36

36/2 = 18

5 0
3 years ago
Im giving 30 points pls help
gayaneshka [121]

Step-by-step explanation:

Pathagory and Theorem

a^2+b^2=c^2

(x-3)^2+(x-4)^2=6^2

expand:

2x^2-14x+25=36

2x^2-14x-11=0

x=(\sqrt{71}+7)/2

perimeter=(x-3)+(x-4)+6=2x-1

insert the value for x into 2x-1

\sqrt{71}+6=perimeter

Hope that helps :)

7 0
3 years ago
Read 2 more answers
The function h(t) = -4.9t² + 19.6t is used to model the height of an object projected in the air where h(t) is the height (in me
goblinko [34]

Answer:

Step-by-step explanation:

when h(t)=0

-4.9 t²+19.6t=0

4.9t(-t+4)=0

either t=0 or t=4

so domain is 0≤t≤4

for range

h(t)=-4.9t²+19.6t

=-4.9(t²-4t+4-4)

=-4.9(t-2)²+19.6

so range is 0≤h≤19.6

5 0
3 years ago
Read 2 more answers
Other questions:
  • Marina wants to make 6 dozen cookies for the school bake sale. how much milk and mix does she need?
    10·1 answer
  • Please help i dont understand
    10·1 answer
  • He following table shows the frequency of outcomes when two distinguishable coins were tossed 5,200 times and the uppermost face
    5·1 answer
  • How do I solve 3 1/2r = 28
    11·2 answers
  • How can you use remainders in divison problems
    9·2 answers
  • An audio books club charges an initial joining fee of $15.00. The cost per audio book is $12.00. The graph shows the cost of bel
    5·1 answer
  • I need friends <br> Drop you snap,insta,Pinterest,VSCO,email whatever of the listed things
    8·2 answers
  • Pls help i will mark brainliest if correctシ♡︎
    11·1 answer
  • The longest side of a triangle is 8 more units than the shortest side. The third side is 4 times the length of the shortest side
    8·1 answer
  • Help pls? Thank you :)
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!