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Consider that f : A rarr B (i) If f(x)...

Consider that `f : A rarr B`
(i) If f(x) is one-one `f(x_(1)) = f(x_(2)) hArr x_(1) = x_(2)` or `f'(x) ge 0` or `f'(x) le 0`.
(ii) If f(x) is onto the range of f(x) = B.
(iii) If f(x) and g(x) are inverse of each other then f(g(x)) = g(f(x)) = x.
Now consider the answer of the following questions.
If f(x) and g(x) are mirror image of each other through y = x and such that f(x) `= e^(x) + x` then the value of g'(1) is

A

`(1)/(2)`

B

2

C

1

D

3

Text Solution

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The correct Answer is:
A
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AAKASH INSTITUTE ENGLISH-RELATIONS AND FUNCTIONS -Assignment (Section - D) Linked Comprehension Type Questions
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  3. Let f(x) be a real valued function such that the area of an equilatera...

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  6. Let f(x) and g(x) be two real valued functions then |f(x) - g(x)| le |...

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  8. The absolute valued function f is defined as f(x) = {{:(x,, x ge 0),(-...

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  9. Consider that f : A rarr B (i) If f(x) is one-one f(x(1)) = f(x(2)) ...

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  11. Consider that f : A rarr B (i) If f(x) is one-one f(x(1)) = f(x(2)) ...

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  13. Let f : [-3, 3] rarr R defined by f(x) = [(x^(2))/(a)] tan ax + sex ax...

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  14. Let f : [-3, 3] rarr R defined by f(x) = [(x^(2))/(a)] tan ax + sex ax...

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