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

Answer:

$f^{-1}(x)=\frac{1}{2}x -\frac{5}{4}$

Step-by-step explanation:

$y=2x+\frac{5}{2}$

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

$x=2y+\frac{5}{2}$

Now, we solve the equation for y

$x=2y+\frac{5}{2}$

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

$\frac{2}{4}x -\frac{5}{4} =y$

Simplify the fraction

$y=\frac{1}{2}x -\frac{5}{4}$

Replace y with f^-1

$f^{-1}(x)=\frac{1}{2}x -\frac{5}{4}$