Question

Which function is the inverse of y=2x+5/2

Answer 1

First you have to change y to x

X= 2y+5/2

Then find y

(X-5/2)/2=y

So (X-5/2)/2 is the. Inverse function

Answer 2

`f^(-1)(x)=(1)/(2)x -(5)/(4)`

Explanation:

`y=2x+(5)/(2)`

To find inverse, we replace x with y and y with x

`x=2y+(5)/(2)`

Now, we solve the equation for y

`x=2y+(5)/(2)`

Multiply the whole equaiton by 2 to remove the denominator 2

`2x= 4y +5`

Now Subtract 5 from both sides

`2x-5 = 4y`

To isolate y, we divide by 4 on both sides

`(2)/(4)x -(5)/(4) =y`

Simplify the fraction

`y=(1)/(2)x -(5)/(4)`

Replace y with f^-1

`f^(-1)(x)=(1)/(2)x -(5)/(4)`