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Given that function f(x) =10x -7 And g(x) =3-¼ x
find the value of
(1)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)?
find the value of
(1)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 that function f(x) =10x -7 And g(x) =3-¼ x find the value of (1)...
1. Calculation of 3f(3) - 2g(3):
Given f(x) = 10x - 7 and g(x) = 3 - ¼ x
Replacing x with 3 in f(x) and g(x):
3f(3) = 3(10(3) - 7) = 3(30 - 7) = 3(23) = 69
2g(3) = 2(3 - ¼ * 3) = 2(3 - 3/4) = 2(9/4) = 18/4 = 4.5
Therefore, 3f(3) - 2g(3) = 69 - 4.5 = 64.5
2. Finding the value of x for which f(x) = 2g(x):
Given f(x) = 10x - 7 and g(x) = 3 - ¼ x
Setting f(x) equal to 2g(x) and solving for x:
10x - 7 = 2(3 - ¼ x)
10x - 7 = 6 - ½ x
10x + ½ x = 6 + 7
10.5x = 13
x = 13/10.5
x = 1.2381
3. Finding the value of p for which f(2p) = g(4p):
Given f(x) = 10x - 7 and g(x) = 3 - ¼ x
Setting f(2p) equal to g(4p) and solving for p:
10(2p) - 7 = 3 - ¼(4p)
20p - 7 = 3 - p
21p = 10
p = 10/21
4. Expressing f-¹(x) and g-¹(x) in terms of a:
To find the inverse functions f-¹(x) and g-¹(x), interchange x and y in the original functions:
f-¹(x) = (x + 7) / 10
g-¹(x) = 12 - 4x
5. Calculation of f-¹(3) - g-¹(4):
Given f-¹(x) = (x + 7) / 10 and g-¹(x) = 12 - 4x
Substitute x = 3 into f-¹(x) and x = 4 into g-¹(x):
f-¹(3) = (3 + 7) / 10 = 10 / 10 = 1
g-¹(4) = 12 - 4(4) = 12 - 16 = -4
Therefore, f-¹(3) - g-¹(4) = 1 - (-4) = 1 + 4 = 5
Given f(x) = 10x - 7 and g(x) = 3 - ¼ x
Replacing x with 3 in f(x) and g(x):
3f(3) = 3(10(3) - 7) = 3(30 - 7) = 3(23) = 69
2g(3) = 2(3 - ¼ * 3) = 2(3 - 3/4) = 2(9/4) = 18/4 = 4.5
Therefore, 3f(3) - 2g(3) = 69 - 4.5 = 64.5
2. Finding the value of x for which f(x) = 2g(x):
Given f(x) = 10x - 7 and g(x) = 3 - ¼ x
Setting f(x) equal to 2g(x) and solving for x:
10x - 7 = 2(3 - ¼ x)
10x - 7 = 6 - ½ x
10x + ½ x = 6 + 7
10.5x = 13
x = 13/10.5
x = 1.2381
3. Finding the value of p for which f(2p) = g(4p):
Given f(x) = 10x - 7 and g(x) = 3 - ¼ x
Setting f(2p) equal to g(4p) and solving for p:
10(2p) - 7 = 3 - ¼(4p)
20p - 7 = 3 - p
21p = 10
p = 10/21
4. Expressing f-¹(x) and g-¹(x) in terms of a:
To find the inverse functions f-¹(x) and g-¹(x), interchange x and y in the original functions:
f-¹(x) = (x + 7) / 10
g-¹(x) = 12 - 4x
5. Calculation of f-¹(3) - g-¹(4):
Given f-¹(x) = (x + 7) / 10 and g-¹(x) = 12 - 4x
Substitute x = 3 into f-¹(x) and x = 4 into g-¹(x):
f-¹(3) = (3 + 7) / 10 = 10 / 10 = 1
g-¹(4) = 12 - 4(4) = 12 - 16 = -4
Therefore, f-¹(3) - g-¹(4) = 1 - (-4) = 1 + 4 = 5
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Given that function f(x) =10x -7 And g(x) =3-¼ x find the value of (1)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 that function f(x) =10x -7 And g(x) =3-¼ x find the value of (1)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 that function f(x) =10x -7 And g(x) =3-¼ x find the value of (1)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 that function f(x) =10x -7 And g(x) =3-¼ x find the value of (1)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 that function f(x) =10x -7 And g(x) =3-¼ x find the value of (1)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 that function f(x) =10x -7 And g(x) =3-¼ x find the value of (1)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 that function f(x) =10x -7 And g(x) =3-¼ x find the value of (1)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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