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Let `f,\ g` be two real functions defined by `f(x)=sqrt(x+1\ )a n d\ g(x)=sqrt(9-x^2)dot` Then describe each of the following function: `g/f`

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`(frac{g}{f})(x)=frac{sqrt(9-x^2) }{sqrt(x+1)}`
`=frac{sqrt(9-x^2)}{sqrt(x+1)}`
Domain of `frac{f}{g}`=domain of `f` `cap` domain of `g`
`=[-1, oo) cap [-3, 3]`
`=[-1, 3)`
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RD SHARMA-FUNCTIONS-Solved Examples And Exercises
  1. Let f,\ g be two real functions defined by f(x)=sqrt(x+1\ )a n d\ g(x)...

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  2. Let f,\ g be two real functions defined by f(x)=sqrt(x+1\ )a n d\ g(x)...

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  3. Let f,\ g be two real functions defined by f(x)=sqrt(x+1\ )a n d\ g(x)...

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  4. Let f,\ g be two real functions defined by f(x)=sqrt(x+1\ )a n d\ g(x)...

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  5. Let f,\ g be two real functions defined by f(x)=sqrt(x+1\ )a n d\ g(x)...

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  6. If f,\ g,\ h are real functions defined by f=sqrt(x+1),\ g(x)=1/x\ a n...

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  7. Let f, g : R -> R be defined, respectively by f(x)=x+1 ,g(x)=2x-3 . Fi...

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  8. Le f:[0,\ oo)->R\ a n d\ g: R->R be defined by f(x)=sqrt(x) and g(x)=x...

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  9. Let f(x)=x^2 and g(x)" "=" "2x" "+" "1 be two real functions....

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  10. Write the range of the real function f(x)=|x|dot

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  11. If f(x)=1-1/x then write the value of f(f(1/x))dot

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  12. If f(x)=4x-x^2, x in R , then write the value of f(a+1)-f(a-1)dot

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  13. If f,\ g,\ h are real functions given by f(x)=x^2,g\ (x)=tanx\ a n d\ ...

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  14. Write the domain and range of function f(x) given by f(x)=1/(sqrt(x-[x...

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  15. Write of the domain and range of f(x)=sqrt(x-[x])dot

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  16. Write the domain and range of function f(x) given by f(x)=sqrt([x]-x).

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  17. Let A and B be any two sets such that n(B)=P, n(A)=q then the total nu...

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  18. Find the values of x for which the functions f(x)=3x^2-1 and g(x)=3+x ...

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  19. If f(x)="cos"((log)e x),t h e nf(x)f(y)-1/2[f(x/y)+f(x y)] has value ...

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  20. Let f(x)=|x-1|dot Then (a)f(x^2)=(f(x))^2 (b) f(x+y)=f(x)+f(y) (c)f(...

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