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Let f: A -> B and g : B -> C be two fun...

Let `f: A -> B and g : B -> C` be two functions and `gof: A -> C` is define statement(s) is true?

A

If gof is one-one, then f anf g both are one-one

B

if gof is one-one, then f is one-one

C

If gof is a bijection, then f is one-one and g is onto

D

If f and g are both one-one, then gof is one-one.

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B, C, D
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Let f:A rarr B and g:B rarr C be two functions and gof:A rarr C is define statement(s) is true?

If f: A-> B and g: B-> C be the bijective function, then (gof)^(-1) is:

Statement I: f : A->B is one - one and g : B->C is a one - one function, then gof :A->C is one - one Statement II : If f:A->B, g:B->A are two functions such that gof=IA and fog=IB, then f=g-1. Statement III : f(x)=sec 2x-tan2x,g(x)=cosec2x-cot2x, then f=g

Let f:A to B and g:B to C be bijection, then (fog)^(-1) =

Let f:A rarr B and g:B rarr C be two functions.Then; if gof is onto then g is onto; if gof is one one then f is one-one and if gof is onto and g is one one then f is onto and if gof is one one and f is onto then g is one one.

Let f:A to A and g:A to A be two functions such that fog(x)=gof (x)=x for all x in A Statement-1: {x in A: f(x)=g(x)}={x in A: f(x)=x}={x in A: g(x)=x} Statement-2: f:A to A is bijection.

If f:A rarr B and g:B rarr C are onto functions show that gof is an onto function.

ARIHANT MATHS-FUNCTIONS-Exercise (Questions Asked In Previous 13 Years Exam)
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  2. If function f(x)=x^(2)+e^(x//2) " and " g(x)=f^(-1)(x), then the value...

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  3. Let F(x) be an indefinite integral of sin^(2)x Statement-1: The fun...

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  4. Find the range of values of t for which 2sint=(1-2x+5x^2)/(3x^2-2x-1)

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  6. The function f:[0,3] to [1,29], defined by f(x)=2x^(3)-15x^(2)+36x+1 i...

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  7. Let f(x)=x^2a n dg(x)=sinxfora l lx in Rdot Then the set of all x sat...

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  8. Let f:(0,1)->R be defined by f(x)=(b-x)/(1-bx), where b is constant s...

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  9. Let f be a real-valued function defined on the inverval (-1,1) such th...

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  10. If X and Y are two non-empty sets where f: X->Y,is function is define...

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  11. If f(x)={x, when x is rational and 0, when x is irrational g(x)={0, wh...

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  12. If f(x)=sinx+cosx, g(x)=x^(2)-1, then g{f(x)} is invertible in the dom...

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  13. Domain of definition of the function f(x)=sqrt(sin^(-1)(2x)+pi/6) fo...

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  14. The range of the function f(x)=(x^2+x+2)/(x^2+x+1),x in R , is (1,oo)...

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  15. If f:[0,infty) rarr [0,infty) " and " f(x)=x/(1+x), then f is

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  16. If f:R to R be defined by f(x) =2x+sinx for x in R, then check the na...

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  17. Let E={1,2,3,4}a n dF-{1,2}dot If N is the number of onto functions fr...

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  18. Suppose f(x)=(x+1)^2forxgeq-1. If g(x) is the function whose graph is ...

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  19. If f:[1,infty) rarr [2,infty) is given by f(x)=x+1/x, " then " f^(-1)(...

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  20. Let f(x0=(1+b^(2))x^(2)+2bx+1 and let m(b) be the minimum value of f(x...

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  21. The domain of definition of function of f(x)=(log(2)(x+3))/(x^(2)+3x+2...

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