Easy interval notation problem... help...?

Question

Use interval notation to give the domain of the function

f(x)= 6/x+5

a) (-infinity,-5)(0,infinity)

b) (-infinity,-5)(-5,infinity)

c) (-infinity,-6)(6,infinity)

d) (-infinity,6)(6,infinity)

e) (-infinity,-5)(5,infinity)

f) None of the above.

yea sorry f(x)= 6 / (x+5)

Answer 1

the answer is ] -infinity,-5[ + ]-5, infinity[

therefore the answer is (b)

that is because -5 is excluded

as denominator mustnt equal to zero in order to be valid

note :takecare of the brackets where for example ]-infinity,-5[
it means that -5 excluded while ]- infinity, -5] it means -5 is included

Answer 2

The way you wrote f(x) is confusing...
If you meant f(x)=6/(x+5), then -5 gives a division by zero, so that's the only point out of the domain of f(x) and the answer is (b).
If you meant f(x)=(6/x)+5, then the answer is (f) and the domain would be (-inf,0)(0,+inf).

Answer 3

Since the only value x cannot be is -5 you want B as your answer because it only skips -5.

Tickler (below) is correct. The way you typed it in would imply that x cannot be zero and (-inf,0)(0,inf) is not an option so if that's truly the problem as written then F is the answer.

Answer 4

b. the domain is all x except -5. The () indicate that -5 is not included.

Answer 5

| 3 + 0.1x | ? 5 The LHS means ± (3 + 0.1x) (i) Taking the + signal, we've : 3 + 0.1x ? 5 => 0.1x ? 5 - 3 => 0.1x ? 2 => x/10 ? 2 => x ? 20 (ii) Taking the - signal, we've : - (3 + 0.1x) = 5 => 3 + 0.1x ? - 5 => 0.1x ? - 5 - 3 => x/10 ? - 8 => x ? - eighty => - eighty ? x Combining (i) and (ii) we get - eighty ? x ? 20 or same as 20 ? x ? - eighty this suggests : x has all authentic values mendacity between - eighty and 20, both inclusive.