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Find the domain of the function `f(x) = (x-1)/(x^(2) + 5x +6)`.

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To find the domain of the function \( f(x) = \frac{x-1}{x^2 + 5x + 6} \), we need to determine the values of \( x \) for which the function is defined. The function will be undefined when the denominator is equal to zero. ### Step-by-Step Solution: 1. **Identify the Denominator**: The denominator of the function is \( x^2 + 5x + 6 \). 2. **Set the Denominator to Zero**: ...
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AAKASH INSTITUTE ENGLISH-RELATIONS AND FUNCTIONS -Try Yourself
  1. Find the domain of definition of the function f(x) = sqrt(64 - x^(2)).

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  2. Find the domain of the function f(x) = (x^(2)+5x+1)/(x^(2)-6x + 8).

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  3. Find the domain of the function f(x) = (x-1)/(x^(2) + 5x +6).

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  4. Find the range: (i) f(x) = 1+x (ii) f(x) = (1)/(x) , x != 0

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  5. Find the range : (i) f(x) = 2x^(2) (ii) f(x) = -x^(2)

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  6. Find the domain of the function y = (x)/(1-x^(2)).

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  7. Find the range of the function y = (x^(2) - 1)/(x-1), x != 1.

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  8. Define the function f : R rarr R by y = f(x) = x^(4), x in R. What is ...

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  9. Define the function f : R rarr R by y = f(x) = x^(5), x in R. What is...

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  10. Given the function f(x) = x^(2) + 2x + 5. Find f(-1), f(2), f(5).

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  11. Given the function f(x) = 2x + 7. Find f(0), f(5), f(7).

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  12. Find the domain and range of |x-3|.

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  13. Find the domain and range of -|x-5|.

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  14. Consider that [] represents greatest integer function. Find the valu...

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  15. Consider that [] represents greatest integer function. [(3)/(5)] + [...

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  16. Let f(x) = x^(3) + 5 and g(x) = 5x + 3 be two real functions. Find (f+...

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  17. Let f(x) = 3x + 8 and g(x) = x^(2) be two real functions. Find (f+g) (...

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  18. If f, g : R rarr R be defined respectively by f(x) = 3x + 2 and g(x) =...

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  19. If f, g : R rarr R be defined respectively by f(x) = 8x + 7 and g(x) =...

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  20. Let f(x) = x^(3) + 6x + 9 and g(x) = x+5 be two functions. Find (f+g) ...

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