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If f(x) = x + tan x and f is inverse of g, then g’(x) is equal to
- a)1/1+(g(x)−x)2
- b)1/1−(g(x)−x)2
- c)1/2+(g(x)−x)2
- d)1/2−(g(x)−x)2
Correct answer is option 'C'. Can you explain this answer?
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If f(x) = x + tan x and f is inverse of g, then g’(x) is equal t...
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If f(x) = x + tan x and f is inverse of g, then g’(x) is equal t...
Explanation:
Given:
- f(x) = x + tan x
- f is the inverse of g
Key Concept:
- If f is the inverse of g, then f(g(x)) = x and g(f(x)) = x
Steps to Find g'(x):
1. Start by finding g(x) by replacing f(x) with x in the given equation:
g(x) = x + tan x
2. To find g'(x), differentiate g(x) with respect to x:
g'(x) = 1 + sec^2x
3. Now, we need to express g'(x) in terms of g(x), so substitute g(x) = x + tan x back into g'(x):
g'(x) = 1 + sec^2(x) = 1 + 1 + tan^2x = 2 + tan^2x
4. Rewrite tan^2x as (g(x) - x)^2:
g'(x) = 2 + (g(x) - x)^2 = 2 + (g(x) - x)^2
5. Therefore, g'(x) is equal to 1/2 + (g(x) - x)^2, which corresponds to option C.
Given:
- f(x) = x + tan x
- f is the inverse of g
Key Concept:
- If f is the inverse of g, then f(g(x)) = x and g(f(x)) = x
Steps to Find g'(x):
1. Start by finding g(x) by replacing f(x) with x in the given equation:
g(x) = x + tan x
2. To find g'(x), differentiate g(x) with respect to x:
g'(x) = 1 + sec^2x
3. Now, we need to express g'(x) in terms of g(x), so substitute g(x) = x + tan x back into g'(x):
g'(x) = 1 + sec^2(x) = 1 + 1 + tan^2x = 2 + tan^2x
4. Rewrite tan^2x as (g(x) - x)^2:
g'(x) = 2 + (g(x) - x)^2 = 2 + (g(x) - x)^2
5. Therefore, g'(x) is equal to 1/2 + (g(x) - x)^2, which corresponds to option C.
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If f(x) = x + tan x and f is inverse of g, then g’(x) is equal t...
This question cannot be asked in CA foundation since we do not have derivatives of trigonometric functions
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If f(x) = x + tan x and f is inverse of g, then g’(x) is equal toa)1/1+(g(x)−x)2b)1/1−(g(x)−x)2c)1/2+(g(x)−x)2d)1/2−(g(x)−x)2Correct answer is option 'C'. Can you explain this answer?
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If f(x) = x + tan x and f is inverse of g, then g’(x) is equal toa)1/1+(g(x)−x)2b)1/1−(g(x)−x)2c)1/2+(g(x)−x)2d)1/2−(g(x)−x)2Correct answer is option 'C'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If f(x) = x + tan x and f is inverse of g, then g’(x) is equal toa)1/1+(g(x)−x)2b)1/1−(g(x)−x)2c)1/2+(g(x)−x)2d)1/2−(g(x)−x)2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If f(x) = x + tan x and f is inverse of g, then g’(x) is equal toa)1/1+(g(x)−x)2b)1/1−(g(x)−x)2c)1/2+(g(x)−x)2d)1/2−(g(x)−x)2Correct answer is option 'C'. Can you explain this answer?.
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