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Let R^+ be the set of all non-negati...

Let `R^+` be the set of all non-negative real numbers. if `f: R^+ rarrR^+` and `g: R^+rarrR^+` are defined as `f(x)=x^2` and `g(x)=+sqrt(x)dot` Find `fog` and `gofdot` Are they equal functions.

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RD SHARMA ENGLISH-FUNCTION-All Questions
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  2. Let f: RvecR and g: RvecR be defined by f(x)=x^2 and g(x)=x+1. Show ...

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  3. Let R^+ be the set of all non-negative real numbers. if f: R^+ rar...

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  5. Let f: RrarrR and g: RrarrR be defined by f(x)=x+1 and g(x)=x-1....

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  6. Show that the exponential function f: R to R , given by f(x)=e^x , i...

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  7. Let A="{"-1,0,1")"a n df={(x , x^2): xA}dot Show that f: AvecA is neit...

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  8. If f: AvecB is an injection such that range of f={a}dot Determine t...

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  9. Which of the following functions from AtoB are one-one and onto? ...

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  10. Prove that the function F : NtoN , defined by f(x)=x^2+x+1 is one-on...

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  11. Let A be any non-empty set. Then, prove that the identity function on ...

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  12. Let A=R-[2] \ a n d \ B=R-[1]. If f: A->B is a mapping defined by f(x)...

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  13. Show that if f1a n df1 are one-one maps from RtoR , then the pro...

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  14. Give examples of two one-one functions f1 and f2 from R to R such t...

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  15. If f,g: R -R are defined respectively by f(x)=x^2+3x+1,g(x)=2x-3, fi...

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  16. If the function f: RvecR be given by f(x)=x^2+2a n dg: RvecR be given ...

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  17. If the function fa n dg are given by f={(1,2),(3,5),(4,1)}a n dg="("(2...

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  18. Suppose f1a n df2 are non=zero one-one functions from RtoRdot is (f...

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  19. Find whether the following functions are one-one or not: f: Rvecgi...

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  20. If the function f and g are given by f={(1,2),(3,5),(4,1)} and g={(2,...

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