UPSC Exam > UPSC Questions > Given the function f(x) =10x-7 and g(x) =3-¼x...
Start Learning for Free
Given the function f(x) =10x-7 and g(x) =3-¼x ,(1)find the values of
(a) f(2)+g(4). (b)f-1) -g(8). (c) 3f(3)-2g(3)
(2) find the value of x for which f (x) =2g(x)
(3) find the value of p for which f(2p)=g(4p)
(4) Express f-¹ (x) and g -¹(x) in terms of a
(5) find the value of f-¹(3)-g-¹(4)?
(a) f(2)+g(4). (b)f-1) -g(8). (c) 3f(3)-2g(3)
(2) find the value of x for which f (x) =2g(x)
(3) find the value of p for which f(2p)=g(4p)
(4) Express f-¹ (x) and g -¹(x) in terms of a
(5) find the value of f-¹(3)-g-¹(4)?
Most Upvoted Answer
Given the function f(x) =10x-7 and g(x) =3-¼x ,(1)find the values of (...
Given functions:
- f(x) = 10x - 7
- g(x) = 3 - ¼x
(1) Find the values of:
(a) f(2) + g(4):
- f(2) = 10(2) - 7 = 20 - 7 = 13
- g(4) = 3 - ¼(4) = 3 - 1 = 2
- f(2) + g(4) = 13 + 2 = 15
(b) f-1(8) - g(8):
- f-1(x) means the inverse function of f(x)
- To find f-1(x), interchange x and y in the equation f(x) = 10x - 7 and solve for y
- f(x) = y = 10x - 7
- x = 10y - 7
- x + 7 = 10y
- y = (x + 7) / 10
- f-1(x) = (x + 7) / 10
- f-1(8) = (8 + 7) / 10 = 15 / 10 = 1.5
- g(8) = 3 - ¼(8) = 3 - 2 = 1
- f-1(8) - g(8) = 1.5 - 1 = 0.5
(c) 3f(3) - 2g(3):
- f(3) = 10(3) - 7 = 30 - 7 = 23
- g(3) = 3 - ¼(3) = 3 - 0.75 = 2.25
- 3f(3) - 2g(3) = 3(23) - 2(2.25) = 69 - 4.5 = 64.5
(2) Find the value of x for which f(x) = 2g(x):
- 10x - 7 = 2(3 - ¼x)
- 10x - 7 = 6 - ½x
- 10x + ½x = 6 + 7
- 10.5x = 13
- x = 13 / 10.5 = 1.238
(3) Find the value of p for which f(2p) = g(4p):
- Substitute the values into the equations and solve for p
- 10(2p) - 7 = 3 - ¼(4p)
- 20p - 7 = 3 - p
- 20p + p = 3 + 7
- 21p = 10
- p = 10 / 21
(4) Express f-1(x) and g-1(x) in terms of a:
- f-1(x) = (x + 7) / 10
- g-1(x) = 4 - 4x
(5) Find
- f(x) = 10x - 7
- g(x) = 3 - ¼x
(1) Find the values of:
(a) f(2) + g(4):
- f(2) = 10(2) - 7 = 20 - 7 = 13
- g(4) = 3 - ¼(4) = 3 - 1 = 2
- f(2) + g(4) = 13 + 2 = 15
(b) f-1(8) - g(8):
- f-1(x) means the inverse function of f(x)
- To find f-1(x), interchange x and y in the equation f(x) = 10x - 7 and solve for y
- f(x) = y = 10x - 7
- x = 10y - 7
- x + 7 = 10y
- y = (x + 7) / 10
- f-1(x) = (x + 7) / 10
- f-1(8) = (8 + 7) / 10 = 15 / 10 = 1.5
- g(8) = 3 - ¼(8) = 3 - 2 = 1
- f-1(8) - g(8) = 1.5 - 1 = 0.5
(c) 3f(3) - 2g(3):
- f(3) = 10(3) - 7 = 30 - 7 = 23
- g(3) = 3 - ¼(3) = 3 - 0.75 = 2.25
- 3f(3) - 2g(3) = 3(23) - 2(2.25) = 69 - 4.5 = 64.5
(2) Find the value of x for which f(x) = 2g(x):
- 10x - 7 = 2(3 - ¼x)
- 10x - 7 = 6 - ½x
- 10x + ½x = 6 + 7
- 10.5x = 13
- x = 13 / 10.5 = 1.238
(3) Find the value of p for which f(2p) = g(4p):
- Substitute the values into the equations and solve for p
- 10(2p) - 7 = 3 - ¼(4p)
- 20p - 7 = 3 - p
- 20p + p = 3 + 7
- 21p = 10
- p = 10 / 21
(4) Express f-1(x) and g-1(x) in terms of a:
- f-1(x) = (x + 7) / 10
- g-1(x) = 4 - 4x
(5) Find
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
Given the function f(x) =10x-7 and g(x) =3-¼x ,(1)find the values of (a) f(2)+g(4). (b)f-1) -g(8). (c) 3f(3)-2g(3)(2) find the value of x for which f (x) =2g(x) (3) find the value of p for which f(2p)=g(4p) (4) Express f-¹ (x) and g -¹(x) in terms of a (5) find the value of f-¹(3)-g-¹(4)?
Question Description
Given the function f(x) =10x-7 and g(x) =3-¼x ,(1)find the values of (a) f(2)+g(4). (b)f-1) -g(8). (c) 3f(3)-2g(3)(2) find the value of x for which f (x) =2g(x) (3) find the value of p for which f(2p)=g(4p) (4) Express f-¹ (x) and g -¹(x) in terms of a (5) find the value of f-¹(3)-g-¹(4)? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Given the function f(x) =10x-7 and g(x) =3-¼x ,(1)find the values of (a) f(2)+g(4). (b)f-1) -g(8). (c) 3f(3)-2g(3)(2) find the value of x for which f (x) =2g(x) (3) find the value of p for which f(2p)=g(4p) (4) Express f-¹ (x) and g -¹(x) in terms of a (5) find the value of f-¹(3)-g-¹(4)? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given the function f(x) =10x-7 and g(x) =3-¼x ,(1)find the values of (a) f(2)+g(4). (b)f-1) -g(8). (c) 3f(3)-2g(3)(2) find the value of x for which f (x) =2g(x) (3) find the value of p for which f(2p)=g(4p) (4) Express f-¹ (x) and g -¹(x) in terms of a (5) find the value of f-¹(3)-g-¹(4)?.
Given the function f(x) =10x-7 and g(x) =3-¼x ,(1)find the values of (a) f(2)+g(4). (b)f-1) -g(8). (c) 3f(3)-2g(3)(2) find the value of x for which f (x) =2g(x) (3) find the value of p for which f(2p)=g(4p) (4) Express f-¹ (x) and g -¹(x) in terms of a (5) find the value of f-¹(3)-g-¹(4)? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Given the function f(x) =10x-7 and g(x) =3-¼x ,(1)find the values of (a) f(2)+g(4). (b)f-1) -g(8). (c) 3f(3)-2g(3)(2) find the value of x for which f (x) =2g(x) (3) find the value of p for which f(2p)=g(4p) (4) Express f-¹ (x) and g -¹(x) in terms of a (5) find the value of f-¹(3)-g-¹(4)? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given the function f(x) =10x-7 and g(x) =3-¼x ,(1)find the values of (a) f(2)+g(4). (b)f-1) -g(8). (c) 3f(3)-2g(3)(2) find the value of x for which f (x) =2g(x) (3) find the value of p for which f(2p)=g(4p) (4) Express f-¹ (x) and g -¹(x) in terms of a (5) find the value of f-¹(3)-g-¹(4)?.
Solutions for Given the function f(x) =10x-7 and g(x) =3-¼x ,(1)find the values of (a) f(2)+g(4). (b)f-1) -g(8). (c) 3f(3)-2g(3)(2) find the value of x for which f (x) =2g(x) (3) find the value of p for which f(2p)=g(4p) (4) Express f-¹ (x) and g -¹(x) in terms of a (5) find the value of f-¹(3)-g-¹(4)? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of Given the function f(x) =10x-7 and g(x) =3-¼x ,(1)find the values of (a) f(2)+g(4). (b)f-1) -g(8). (c) 3f(3)-2g(3)(2) find the value of x for which f (x) =2g(x) (3) find the value of p for which f(2p)=g(4p) (4) Express f-¹ (x) and g -¹(x) in terms of a (5) find the value of f-¹(3)-g-¹(4)? defined & explained in the simplest way possible. Besides giving the explanation of
Given the function f(x) =10x-7 and g(x) =3-¼x ,(1)find the values of (a) f(2)+g(4). (b)f-1) -g(8). (c) 3f(3)-2g(3)(2) find the value of x for which f (x) =2g(x) (3) find the value of p for which f(2p)=g(4p) (4) Express f-¹ (x) and g -¹(x) in terms of a (5) find the value of f-¹(3)-g-¹(4)?, a detailed solution for Given the function f(x) =10x-7 and g(x) =3-¼x ,(1)find the values of (a) f(2)+g(4). (b)f-1) -g(8). (c) 3f(3)-2g(3)(2) find the value of x for which f (x) =2g(x) (3) find the value of p for which f(2p)=g(4p) (4) Express f-¹ (x) and g -¹(x) in terms of a (5) find the value of f-¹(3)-g-¹(4)? has been provided alongside types of Given the function f(x) =10x-7 and g(x) =3-¼x ,(1)find the values of (a) f(2)+g(4). (b)f-1) -g(8). (c) 3f(3)-2g(3)(2) find the value of x for which f (x) =2g(x) (3) find the value of p for which f(2p)=g(4p) (4) Express f-¹ (x) and g -¹(x) in terms of a (5) find the value of f-¹(3)-g-¹(4)? theory, EduRev gives you an
ample number of questions to practice Given the function f(x) =10x-7 and g(x) =3-¼x ,(1)find the values of (a) f(2)+g(4). (b)f-1) -g(8). (c) 3f(3)-2g(3)(2) find the value of x for which f (x) =2g(x) (3) find the value of p for which f(2p)=g(4p) (4) Express f-¹ (x) and g -¹(x) in terms of a (5) find the value of f-¹(3)-g-¹(4)? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup