Answer:
[tex]f^{-1}[/tex](x) = [tex]\frac{x-3}{2}[/tex]
Step-by-step explanation:
Let y = f(x) and rearrange making x the subject
y = 2x + 3 ( subtract 3 from both sides )
y - 3 = 2x ( divide both sides by 2 )
[tex]\frac{y-3}{2}[/tex] = x
Change y back into terms of x, hence
[tex]f^{-1}[/tex](x ) = [tex]\frac{x-3}{2}[/tex]
Keep in mind that f(x) means the same thing as y so...
y = 2x + 3
To find the inverse operation you switch the places of x and y like so...
x = 2y + 3
Now you must solve for y. To start off you must subtract 3 to both sides.
x - 3 = 2y + 3 - 3
x - 3 = 2y
Now divide 2 to both sides to completely isolate y
(x - 3) / 2 = 2y / 2
[tex]\frac{1}{2} x - \frac{3}{2}[/tex] = y
OR
[tex]\frac{x}{2} -\frac{3}{2}[/tex] = y
Hope this helped!
~Just a girl in love with Shawn Mendes
