Algebra - Functions

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Find the domain:

a) [sqrt(x+3)]+[5x^2-180]

b) [sqrt(x+3)]/[5x^2-180]

c) (8x+9)(9x+8)

d) (8x+9)/(9x+8)

e) [sqrt(x+2)](5x^2-245)

f) [sqrt(x+2)]/(5x^2-245)

  • Algebra - Functions -

    all polynomials have domain of (-∞,+∞)

    √u has domain u >= 0

    rational functions have domains which exclude where the denominator is zero.

    Keeping that in mind, I'll do (b), and the rest should be easy.

    √(x+3) needs x+3 >= 0, or x >= -3
    the domain also excludes x=±6, since then 5x^2-180=0, and you cannot divide by zero. -6 is already excluded by the √, so the domain is [-3,6)∪(6,∞)

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