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Letf: A rarr B be a function then show t...

Letf: `A rarr B` be a function then show that f is a bijection if and only if there exists a function `g: B rarr A` such that fog = `I_B & gof = I_A` & in this case g = `f^(-1)`

A

one-one

B

onto

C

one-one and onto

D

None of these

Text Solution

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The correct Answer is:
C
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DISHA PUBLICATION-RELATIONS AND FUNCTIONS-2-EXERCISE-2: CONCEPT APPLICATOR
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  11. Let f(x)=(x+1)^2-1, xgeq-1. Then the set {x :f(x)=f^(-1)(x)} is {0,1,(...

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  15. Let f(x)=a x+ba n dg(x)=c x+d , a!=0. Assume a=1,b=2. If (fog)(x)=(gof...

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  17. "If "f:R to R, g:R and h:R to R be three functions are given by f(x)=x...

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  18. Let g(x)=1+x-[x] and f(x)={{:(-1",", x lt 0),(0",",x=0),(1",", x gt 0)...

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  19. Which of the following functions is the inverse of itself? f(x)=(1-x)/...

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