Question

PLEASE HELP:

Answer 1

can you write it in numbers?

Answer 2

@elijahrich1113 f(x)=13/10-x

Answer 3

Think: When are fractions not defined? What number can we not divide by?

Answer 4

@jim_thompson5910 please help, no one has helped me all day!

Answer 5

The function is this
\[\Large f(x) = \frac{13}{10-x}\]
right?

Answer 6

yes

Answer 7

Recall that you CANNOT divide by zero. You cannot have something like \(\Large \frac{1}{0}\)


Zero must NEVER be in the denominator

Answer 8

The question I have for you @iwanttogotostanford is this: what value of x makes the denominator \(\Large 10-x\) equal to zero?

Answer 9

so basically I'm asking you to solve
\[\Large 10-x = 0\]
for x

Answer 10

ok so it would end up to be x= x+10

Answer 11

if you added x to both sides, you'd end up with \(\Large x = 10\)

Answer 12

sorry i meant the other x to be a 0

Answer 13

so if \(\Large x = 10\), then \(\Large 10-x\) is equal to 0

Answer 14

x = 10 causes a division by zero error so we must kick it out of the domain. No other x value gives us this trouble, so we can keep any other real number we want

Answer 15

oh ok i see that

Answer 16

In set notation, you would say that the domain is
\[\Large \left\{x|x\in\mathbb{R} \ , \ x \ne 10\right\}\]
which is fancy math speak for "x is any real number but NOT 10. So anything but 10"

Answer 17

so it would be all real numbers except for 10, correct?

Answer 18

In interval notation, the domain would be written as
\[\Large \left(-\infty,10\right)\cup\left(10,\infty\right)\]
which is the interval from -infinity to +infinity, but we take out 10. So we form a hole at 10 on the number line and keep everything else.

Answer 19

`so it would be all real numbers except for 10, correct?`
yes @iwanttogotostanford

Answer 20

thank yoU! you are always the best help honestly. Clear and concise help ! I appreciate it. Can i please ask you a few more? You really help me learn the concepts !

Answer 21

if you have any other questions, post them one at a time in a new thread (one question per post)

Answer 22

Then tag me in any question you get stuck on