Answer:
[tex]f^{-1}(x)=\frac{1}{2}x -\frac{5}{4}[/tex]
Step-by-step explanation:
[tex]y=2x+\frac{5}{2}[/tex]
To find inverse, we replace x with y and y with x
[tex]x=2y+\frac{5}{2}[/tex]
Now, we solve the equation for y
[tex]x=2y+\frac{5}{2}[/tex]
Multiply the whole equaiton by 2 to remove the denominator 2
[tex]2x= 4y +5[/tex]
Now Subtract 5 from both sides
[tex]2x-5 = 4y[/tex]
To isolate y, we divide by 4 on both sides
[tex]\frac{2}{4}x -\frac{5}{4} =y[/tex]
Simplify the fraction
[tex]y=\frac{1}{2}x -\frac{5}{4}[/tex]
Replace y with f^-1
[tex]f^{-1}(x)=\frac{1}{2}x -\frac{5}{4}[/tex]
