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If f(g(x)) = x and g(f(x)) = x then g(x)...

If f(g(x)) = x and g(f(x)) = x then g(x) is the inverse of `f(x) . (g'(x))f'(x) = 1 implies g'(f(x))=1/(f'(x))`
Let us consider a real value bijective function g(x) sun that g'(x) = `sin^2 (x+pi/4) +2 cos (x -pi/4) and g(pi/4) =3` then value of `(g^(-1))(3)` is

A

`1/5`

B

`1/2`

C

`1/3`

D

0

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D
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Knowledge Check

  • If f(g(x)) = x and g(f(x)) = x then g(x) is the inverse of f(x) . (g'(x))f'(x) = 1 implies g'(f(x))=1/(f'(x)) If f(x) = x^3 +x^2 +log_ex and g is inverse of f then 6'g(6) is equal to

    A
    1
    B
    2
    C
    3
    D
    4

  • If f(g(x)) = x and g(f(x)) = x then g(x) is the inverse of f(x) . (g'(x))f'(x) = 1 implies g'(f(x))=1/(f'(x)) Let g(x) be the inverse of f(x) such that f'(x) =1/(1+x^5) ,then (d^2(g(x)))/(dx^2) is equal to

    A
    `1/(1+(g(x))^5)`
    B
    `(g'(x))/(1+(g(x))^5)`
    C
    `5(g(x))^4+(1+(g(x))^5)`
    D
    `1+g(x))^5`

  • If f(x) = (x)/(1 + x) and g(x) = f(f(x)), then g(x) is equal to

    A
    `(1)/((2x + 3)^(2))`
    B
    `(1)/((x + 1)^(2))`
    C
    `(1)/(x^(2))`
    D
    `(1)/((2x + 1)^(2))`

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