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
lianna [129]
3 years ago
10

How to find (c,d,e)Please do a step by step working.Thank you.

Mathematics
1 answer:
Natasha2012 [34]3 years ago
8 0
(a)
The inverse is when you swap the variables and solve for y.
g(t) = 2t - 1 (Note: g(t) represents y)
rewrite as: y = 2t - 1
swap the variables: t = 2y - 1
solve for y: t + 1 = 2y
                   \frac{t + 1}{2} = y
Answer for (a): g^{-1}(t) =  \frac{t + 1}{2}

(b)
Same steps as part (a) above:
h(t) = 4t + 3
rewrite as: y = 4t + 3
swap the variables: t = 4y + 3
solve for y: y =\frac{t - 3}{4}

Answer for (b): h^{-1}(t) = \frac{t - 3}{4}

(c)
g^{-1} ( h^{-1}(t)) =  g^{-1} (\frac{t - 3}{4})
replace all t's in the g^{-1}(t) equation with \frac{t - 3}{4}
 g^{-1} (\frac{t - 3}{4}) = \frac{ \frac{t-3}{4} + 1}{2}
= \frac{ \frac{t-3}{4} +  \frac{4}{4}}{2} = \frac{ \frac{t - 3 + 4}{4}}{2} = \frac{ \frac{t + 1}{4}}{2} =  \frac{t + 1}{8}
Answer for (c): g^{-1} ( h^{-1}(t)) = \frac{t + 1}{8}

 (d)
h(g(t)) = h(2t - 1) = 4(2t - 1) + 3 = 8t - 4 + 3 = 8t - 1
Answer for (d): h(g(t)) = 8t - 1

(e)
h(g(t)) = 8t - 1
   y = 8 t - 1
   t = 8y - 1
  t + 1 = 8y
\frac{t + 1}{8} = y
Answer for (e): inverse of h(g(t)) = \frac{t + 1}{8}
 
























You might be interested in
If it takes Andre 4 minutes to swim five laps how much will it take him to swim 22 laps at the same speed
Musya8 [376]

Answer:

17.6 minutes

Step-by-step explanation:

\frac{4}{5} = \frac{x}{22}

5x=22

x=\frac{22}{5}

4(\frac{22}{5} ) = \frac{88}{5} = 17.6

5 0
3 years ago
Solve log660 – log630.
Misha Larkins [42]
The answer would be log62...
6 0
3 years ago
Read 2 more answers
Which pair of ratios are equal?6/15 and 3/17 3/4 and 9/11 2/5 and 12/35 or 2/3 and 8/12
Elanso [62]
The last pair.
Because 2*4/3*4=8/12
7 0
3 years ago
Four more than a number is half the number
eduard

Answer:

b

Step-by-step explanation:

7 0
3 years ago
-3 | -8n – 8 | = -120<br><br> Can you guys solve for absolute value??
alexandr1967 [171]

Answer:

n = -6 or n = 4.

Step-by-step explanation:

-3 | -8n – 8 | = -120

Divide both sides by -3:

| -8n – 8 |  = 40

This gives us 2 equations because the expression in the absolute signs can be positive or negative:

-8n - 8 = 40

so -8n = 48

n = -6.

and

-8n - 8 = -40

-8n = -32

n = 4.

3 0
3 years ago
Other questions:
  • What is the answer for -8(w-6=32
    6·1 answer
  • 12 out of 20 doctors agree 15 out of 30 don't agree
    13·1 answer
  • Morty buys and sells computer parts. He bought 2 monitors for $25.00 each and later sold them for $88.00 each. He bought 4 cases
    8·2 answers
  • A circle has a radius of 4 x^3 y^5 cm. The area of a circle can be found using A equals pi r^2
    13·1 answer
  • Mary owns 13 shares of a certain stock. Yesterday the value of each share went up by 4 dollars. What was the total change in val
    12·1 answer
  • -2/11 ÷ -3 /11 remember to simplify
    13·1 answer
  • Whats is 2 times 2 minus 5
    14·2 answers
  • What does 4x-2y=2 equal to step by step
    12·2 answers
  • PLEASE HELP ME ON MATH ASAP
    10·2 answers
  • Can someone help me pls I need help realllll bad right now someone pls
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!