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
Fudgin [204]
4 years ago
14

Find f(x) and g(x) so that the function can be described as y = f(g(x)). y = Four divided by x squared. + 9

Mathematics
1 answer:
Igoryamba4 years ago
5 0

•   Interpretation I:

Find f and g, so that

                           4
(f o g)(x)  =  —————
                       x² + 9


Well, there is more than one possibility.

                                                     4
For instance, It can be:  f(x)  =  ——  and  g(x) = x² + 9,
                                                     x


and then you have

                          
(f o g)(x)  =  f[ g(x) ]

                         4
(f o g)(x)  =  ————
                       g(x)


                         4
(f o g)(x)  =  —————        ✔
                      x² + 9

                                                                                    4
Another possibility for that composition:   f(x)  =  —————  and  g(x) = x²,
                                                                                 x + 9

and for those, you get

(f o g)(x)  =  f[ g(x) ]

                             4
(f o g)(x)  =  ———————
                     [ g(x) ]² + 9

                           4
(f o g)(x)  =  —————          ✔
                       x² + 9


As you can see above, there are many ways to find f and g, so the composition of those is  (f o g)(x) = 4/(x² + 9).

—————

•  Interpretation II:

Find f and g, so that

                      4
(f o g)(x)  =  ——  +  9
                      x²

                                                            4
It can be:   f(x) = x + 9  and  g(x)  =  ——
                                                            x²

and then you have

(f o g)(x) = f[ g(x) ]

(f o g)(x) = g(x) + 9

                     4
(f o g)(x)  =  ——  +  9
                     x²

                                                                             2
or it could be also:   f(x) = x² + 9  and  g(x)  =  ——
                                                                             x


and you have again

(f o g)(x) = f[ g(x) ]

(f o g)(x) = [ g(x) ]² + 9

(f o g)(x) = [ 2/x ]² + 9

(f o g)(x) = (2²/x²) + 9

                      4
(f o g)(x)  =  ——  +  9          ✔
                     x²


As you can see above, there are many ways to find f and g, so the composition of those is  (f o g)(x) = (4/x²) + 9.


I hope this helps. =)


Tags:  <em>composite functions rational quadratic linear function algebra</em>

You might be interested in
Solve these problems using base ten blocks to show your work. Use the pen feature to draw a picture. Type your answer in the tex
aniked [119]
You have 0.15 + 0.36 just like you would just add normal so 1. Would be 0.51 and the other one would be 0.15
8 0
3 years ago
Read 2 more answers
What percent of 16 is 10
e-lub [12.9K]

62.5 is the answer to your question

8 0
4 years ago
D.<br> X= 1<br> 13.<br> Find the vertex: y=-(x+6)² + 2
adelina 88 [10]

Answer:

the vertex of this parabola is at (-6, 2).

Step-by-step explanation:

Compare the given y=-(x+6)² + 2 with the standard vertex form:

                                 y = a(x - h)^2 + k.  We see that

                                  h must be -6 and k must be 2.

Thus the vertex of this parabola is at (-6, 2).

6 0
4 years ago
Help me! I'm stuck.
gregori [183]
<span>Zinch.com. Zinch is a college students one-stop-shop for scholarships that are creative, easy and fun to apply for and win. ...Fastweb.com. ...ScholarshipPoints.com. ...Cappex.com. ...<span>Scholarships.com.</span></span>
8 0
3 years ago
Write 10,100,or 1,000 to make each statement true. A. 1,000,000 is--------------- times greater than 10,000.
VashaNatasha [74]

Answer:100

Step-by-step explanation: 10 x 10000 = 100000 x 10 = 1000000. If we multiply 100 x 10000, we got 1 million

4 0
3 years ago
Other questions:
  • How do you solve 2 7/10+ 2 4/5?
    5·1 answer
  • Find the value of x.<br><br> log 3 x=4
    7·1 answer
  • Simplify the problem​
    12·2 answers
  • 3. For each of the following, indicate if it is a problem involving permutations, combinations, or neither, and then answer the
    15·1 answer
  • Write the domain and range as inequalities.
    8·1 answer
  • 3x +1 = 4<br> Solve the equation
    9·1 answer
  • Each variable indicates different weights. Which weight can you find? Find it.
    9·1 answer
  • How do you write a graph that passes through the point (5, -1) and has a slope of 2 in Slope Intercept Form?
    13·2 answers
  • In an orchard, there are 16 apple trees, 22 orange trees, and a cherry tree. What is the ratio of apple trees to orange trees? O
    12·2 answers
  • Which is greater?<br> B. 42%<br> A. 0.482
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!