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Let f be an injective function with doma...

Let f be an injective function with domain `{x, y, z}` and range `{1, 2, 3}` such that exactly one of the following statements is correct and the remaining are false. `f(x)=1, f(y) ne1, f(z) ne 2`. The value of `f^(-1)(1)` is

A

x

B

y

C

z

D

none

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DIPTI PUBLICATION ( AP EAMET)-FUNCTIONS-EXERCISE 1A(FUNCTIONS)
  1. If f from R into R defined by f(x)=x^(3)-1, then f^(-1){-2, 0, 7}=

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  2. f:R rarrR defined by f(x)=x^(3)+x^(2)-x-1. Then the inverse image set ...

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  3. Let f be an injective function with domain {x, y, z} and range {1, 2, ...

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  4. If f={(a, 0), (b, 2), (c, -3)}, g={(a, -1), (b, 1), (c, 2)} then 2f-3g...

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  5. If f={(a, 1), (b, -2), (c, 3)}, g={(a, -2), (b, 0), (c, 1)} then f^(2)...

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  6. If f={(a, 0), (b, -2), (c, 3)}, g={a, -2), (b, 0), (c,1)} then f//g=

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  7. If f={(-2, 4), (0, 6), (2, 8)} and g={(-2, -1), (0, 3), (2, 5)}, then ...

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  8. If f:{(1, 2), (2,3), (3, 1)}, then fof=

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  9. If f={(1,a), (2, b), (1, b), (3,c), (1,c)}, g=(a, p), (b,r), (c,q), (c...

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  10. If f(x)=2x-1, g(x)=x^(2), then (3f-2g)(x)=

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  11. If f(x)=x^(2), g(x)=x^(2)-5x+6 then (g(2)+g(2)+g(0))/(f(0)+f(1)+f(-2))...

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  12. f(x)=1, if x rational, =0, if x is irrational. Then (f(1//2)+f(sqrt5...

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  13. Two functions f:Rrarr R, g:R rarr R are defined as follows : f(x)={{...

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  14. If f:Rrarr R is defined by f(x)=3x-2, then (f(o)f) (x)+2=

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  15. If f(x)=sqrt(x^(3)-1) and g(x)=root(3)(x^(2)+1), then (fog)(x)=

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  16. f:R rarr R, defined by f(x)=sinx and g:R rarrR, defined by g(x)=x^(2),...

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  17. If f:R rarr R, g:R rarr R are defined by f(x)=x^(2)+2x-3, g(x)=3x-4, t...

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  18. If f:R rarr R, g:R rarr R are defined by f(x)=4x-1, g(x)=x^(3)+2, then...

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  19. If f:R rarrR, g:R rarrR are defined by f(x)=3x-2, g(x)=x^(2)+1, then (...

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  20. Let g(x)=1+x-[x] and f(x)=-1 if x lt 0 =0 if x=0 then f[g(x)]= =1 ...

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