Question

Which of the following expressions is the inverse of the function y= x+5/7

a) y= x+7/5
b) y= x-5/7
c) y=5x-7
d) y=7x-5

Answer 1

solve for x

Answer 2

if the equation is y=x+5/7 to do that you just need to subtract 5/7 on both sides

if the equation is y=(x+5)/7 I would first multiply 7 on both sides and if is this equation you have one more step remaining after that

Answer 3

its the first one but im not sure how to divide the 5/7 to both sides..sorry can u help?

Answer 4

no subtraction is not division

Answer 5

Here is an example:
\[y=x+a \\ \text{ Subtract } a \text{ on both sides } \\ y-a=x \\ \text{ or other way around } x=y-a \\ \text{ then you can interchange } x \text{ and } y \\ y=x-a \text{ this is the inverse of } y=x+a\]

Answer 6

sorry read it wrong so it would be 5/7y = x?

Answer 7

well you didn't exactly subtract 5/7 on the left hand side
it appears you multiply 5/7 on left hand side

Answer 8

im so confused can u just do this one for me so I can use it as an example for my other problems? im not cheating it would be easier for me to understand. im sorry.

Answer 9

oh so you didn't understand the example above either?

Answer 10

oh wait got it hold on

Answer 11

y-5/7=x?

Answer 12

\[\text{ pretend } a=\frac{2}{3} \\ y=x-\frac{2}{3} \text{ is the inverse of } y=x+\frac{2}{3} \\ \text{ if work needs \to be shown we can go through the process again } \\ \text{ pretend we have } \\ y=x+\frac{2}{3} \\ \text{ subtract } \frac{2}{3} \text{ on both sides } \\ y-\frac{2}{3}=x \\ x=y-\frac{2}{3} \\ \text{ interchange } x \text{ and } y \\ y=x-\frac{2}{3} \\ \text{ So we know } y=x-\frac{2}{3} \text{ is the inverse of } y=x+\frac{2}{3}\]

Answer 13

and yes your a=5/7

Answer 14

\[y=x+\frac{5}{7} \\ \text{ subtract} \frac{5}{7} \text{ on both sides } \\ y-\frac{5}{7}=x \\ x=y-\frac{5}{7}\]
yep now just interchange x and y

Answer 15

interchange?

Answer 16

replace x with y and y with x

Answer 17

pull the old switch a roo

Answer 18

y= x+5/7

switch the x and the y
and then solve for y

Answer 19

\[y=x-\frac{5}{7}\]

Answer 20

you can solve for x
then switch
but either way

Answer 21

I was taught to switch first then solve for y :)

Answer 22

y = x-5/7

Answer 23

but that works too... even though I got used to one technique @freckles

Answer 24

here is another example @Barrelracing of finding inverse of a linear function
\[y=\frac{x+5}{7} \\ \text{ multiply both sides by } 7 \\ 7y=x+5 \\ \text{ then subtract} 5 \text{ on both sides } 7y-5=x \\ \text{ now interchange } x\text{ and } y \\ 7x-5=y \\ y=7x-5 \text{ is the inverse of } y=\frac{x+5}{7}\]

Answer 25

there is a reason I like to do the switch step last @UsukiDoll

Answer 26

but a linear example is not the best example to show why

Answer 27

By the way @Barrelracing you look wonderful.