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Let f: R rarr R and g: R rarr R be two g...

Let `f: R rarr R` and `g: R rarr R` be two given functions such that f is inective and g is surjective. Then which of the following is injective

A

gof

B

fog

C

gog

D

fof

Text Solution

Verified by Experts

The correct Answer is:
D
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Knowledge Check

  • Let f: R rarr R and g:R rarr R be two one-one and onto functions such that they are the mirror images of each other about the line y=a . If h(x)=f(x)+g(x) then h(x) is

    A
    one-one onto
    B
    one-one into
    C
    many-one into
    D
    many-one onto

  • Let f and g be two diffrentiable functions on R such that f'(x) gt 0 and g'(x) lt 0 for all x in R . Then for all x

    A
    `f(g(x)) gt f(g(x-1))`
    B
    `f(g(x)) gt f(g(x+1))`
    C
    `g(f(x)) gt g(f(x+1))`
    D
    `g(f(x)) gt g(f(x+1))`

  • Let f: R rarr R, g: R rarr R be two functions given by f(x)=2x-3, g(x)=x^(3)+5 . Then , (fog)^(-1) is equal to

    A
    `((x+7)/(2))^(1//3)`
    B
    `(x- 7/2)^(1//3)`
    C
    `((x-2)/(7))^(1//3)`
    D
    `((x-7)/(2))^(1//3)`

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    If f : R rarr R and g: R rarr R are given by f(x)=|x| and g(x)={x} for each x in R , then |x in R : g(f(x)) le f(g(x))}=

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