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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: `(fg)(x)`

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`(fg)(x)=f(x)g(x)`
`(fg)(x)=sqrt(x+1)sqrt(9-x^2)`
`=sqrt[(x+1)(9-x^2)]`
`=sqrt(9+9x-x^2-x^3)`
The domain of `fg`=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. Let f,\ g be two real functions defined by f(x)=sqrt(x+1\ )a n d\ g(x)...

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

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

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

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

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

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

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

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

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

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

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

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

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