Question

Match the following 1-1 functions with its inverse.

x+5/7


x-7/3

Answer 1

@mathway

Answer 2

Match the following 1-1 functions with its inverse.

Answer 3

@vera_ewing

Answer 4

Match the following 1-1 functions with its inverse.

x+5/7


x-7/3

@vera_ewing

Answer 5

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


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

it appears you multiply 5/7 on left hand side

y-5/7=x?
yes your a=5/7

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

replace x with y and y with x

y= x+5/7 switch the x and the y and then solve for y

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


you can solve for x then switch but either way


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