Question

the domain and range? medal if you help!

I learned the way where it is like y ≥ -2 and x ≥ 0 or where all numbers except x=2 or something like that. Can you please help!

1. f(x)= 1/(x+1)
2. f(x)= 1/(x-2) +1
3. f(x)= 2/x -3
4. f(x)= 1/(x-4) +3
5. f(x)= 1/(x+5) +2

Answer 1

make sure the denominator is never zero
i.e. set the denominator equal to zero and solve, then say all real numbers except that one

Answer 2

for example
\[f(x)=\frac{1}{x+1}\] set
\[x+1=0\] get \[x=-1\] so all real numbers except \(-1\)

Answer 3

The domain is the numbers you can enter in to an equation.

The range is the numbers you can get out of an equation.

To find the domain of an equation you must know some rules which govern equations, here are a short list:

- You cannot divide by 0: 1/x -> x cannot be 0
- You cannot take the square root of a negative number: sqrt(x) -> x cannot be negative
- You cannot take the nautral log of a negative number or 0: ln(x) -> x cannot be 0 or negative

Answer 4

@satellite73 that makes sense so what about the range ? how do I do that exactly

Answer 5

@chaise okay, i'll keep that in my notes

Answer 6

@satellite73 I think I got all real numbers except 0 for the range..?

Answer 7

That is correct for the first one: 1/(x+1) :)

Answer 8

and then domain is all real numbers except 2 and range is all real numbers except 1

for number two @chaise I think from here I got it if this is correct :)

Answer 9

no that is not the range

Answer 10

a fraction is only zero when the numerator is
your fraction has a 1 in the numerator so it is never zero
range is all numbers except 1

Answer 11

oops i mean all numbers except 0!!