Question

Help Medal!

Answer 1

\[y=\frac{ 2+5x }{ 3x }\]

Answer 2

How do you find the Range

Answer 3

@Nnesha

Answer 4

@phi

Answer 5

@ybarrap

Answer 6

@pooja195

Answer 7

First find those point where the function does not have a value. Look at the denominator. What value can x NOT be?

Answer 8

0

Answer 9

Correct! So all other values are allowed. Right?

Answer 10

Then I got {yly cannot = -2/5}

Answer 11

But My book says {yly cannot = 5/3}

Answer 12

D: {x l x cannot = 0}

Answer 13

Similarly, for the range
$$
y=\frac{ 2+5x }{ 3x }\\
\implies x = \frac{2}{3 y-5} \text{ and } 3y\ne5\\
\implies y\ne \frac{3}{5}
$$
All other values of y are allowed.

So what is the range?

Answer 14

Correction:
$$
y\ne \cfrac{5}{3}
$$

Answer 15

Why did you do the inverse though

Answer 16

We solved for x because we wanted to find the valid values of y and this will help us find it:
$$
y=\frac{ 2+5x }{ 3x }\\
3xy=2+5x\\
3xy-5x =2\\
x(3y-5)=2\\
x=\cfrac{2}{3y-5}
$$
This shows us that y can not be equal to 5/3 but all other values are ok.

Answer 17

If y = 5/3 then x will "blow up" and that's not good