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
Ksju [112]
2 years ago
15

The functions it f and g are defined for all real values of x by f(x)=x^2+4ax+a^2 and g(x)=4x-2a where a is a positive constant.

Given that fg(3)=69 find the value of a and hence find the value of x such that g^-1(x) =x
Mathematics
1 answer:
ycow [4]2 years ago
7 0

Answer:

Below in bold.

Step-by-step explanation:

We find fg(x) by replacing the x in f(x) by g(x), so:

fg(x) = (4x - 2a)^2 + 4a(4x - 2a) + a^2

fg(3) = 89 so:

(4(3) - 2a)^2 + 4a(4(3) - 2a) + a^2 = 69

(12 - 2a)^2 + 48a - 8a^2 + a^2 - 69 = 0

144 - 48a + 4a^2 + 48a - 8a^2 + a^2 - 69 = 0

-3a^2  + 75 = 0

-3a^2  = -75

a^2 = 25

a = 5.

Now g(x) = 4x - 2(5) = 4x - 10.

Finding g-1(x);

4x = g(x) + 10

x = (g(x) + 10)/4

So g-1(x) = (x + 10)/4

When g-1(x)= x

x = (x +10)/4

4x = x + 10

3x = 10

x = 10/3.

You might be interested in
Can someone help with #28
Mariana [72]
It would be 50

130+180= 310

360-310= 50

You get 180 from the missing side by 70 that becomes 180.
4 0
3 years ago
[2P-3.) ^2+(2P+3)^2<br>​
WINSTONCH [101]

Answer:

[2P-3.) ^2+(2P+3)^2[2P-3.) ^2+(2P+3)^2[2P-3.) ^2+(2P+3)^2

4 0
3 years ago
Farrah needs an electrician and must decide between 2 companies. For a service visit, Company A charges $50 to send an electrici
ss7ja [257]
Company B. Its kinda commen sense.
4 0
3 years ago
Read 2 more answers
Since he's made of metal, Moby weighs a lot. In fact, Tim's weight is only 4 percent of Moby's weight. If Tim weighs 50 kg, how
Ivanshal [37]

Answer:

Moby weighs 1250Kgs

Step-by-step explanation:

Tim is 4% of Moby so

T =4%m

if T is for Tim and Tim weighs 50kgs then

50=4%m

100/4=25

25*50=1250

M = 1250Kgs

8 0
3 years ago
What is the arc measure of YWZ in<br> degrees?<br> (5w+4)<br> (11w)
Rashid [163]

Answer:

59 degrees

Step-by-step explanation:

In the figure below, XZ is a diameter of circle A.

Since the Angles (5w+4) and (11w) forms a straight line, then:

(5w+4)^\circ+(11w)^\circ=180^\circ\\5w+11w+4=180\\16w=180-4\\16w=176\\w=\frac{176}{16}\\ w=11

Therefore, the arc measure of YZ will be:

5w+4=5*11+4=59^\circ

4 0
3 years ago
Other questions:
  • There were 9500 spectators at a football match. 6375 of them were men. Of the remaining spectators, there were 4 times as many c
    8·1 answer
  • I dont know how to do this,can someone please help me?
    15·1 answer
  • Subtract<br> (2x²+5) - (4x - 3)
    5·2 answers
  • At a price of $p the demand x per month (in multiples of 100) for a new piece of software is given by x 2 + 2xp + 4p 2 = 5200. B
    8·1 answer
  • Find f(g(4)).<br> fg(4)) =
    5·1 answer
  • A density curve for all the possible weights between 0 pounds and 10 pounds is in the shape of a rectangle. What is the height o
    7·1 answer
  • Shape p is translated to shape Q using vector (a b). <br> Please find A. <br> Photo attached.
    8·1 answer
  • 12) 8x - 2 = -9 + 7x<br> Answer
    9·1 answer
  • Every square is a trapezoid. Is this true or false?
    11·1 answer
  • Pls help this is on edge
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!