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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)?
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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
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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)?.
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