Answer:
The inverse of y is
[tex]\textbf{f}^{( -1 )}( x ) = \frac{\textbf{x-5}}{\textbf{3}}[/tex]
Step-by-step explanation:
To Find the inverse of [tex]y = 3x+5[/tex]
STEP 1: Stick a "y" in for the "f(x)"
y = 3x+5
STEP 2: Switch the x and y ( because every (x, y) has a (y, x) partner! ):
[tex]x = 3y+5[/tex]
STEP 3: Solve for y:
[tex]{x-5}=3y[/tex]
[tex]y=\frac{x-5}{3}[/tex]
STEP 4: Stick in the inverse notation,[tex]f^{( -1 )}( x )[/tex]
[tex]f^{( -1 )}( x ) =\frac{x-5}{3}[/tex]
Therefore the inverse of y is
[tex]f^{( -1 )}( x ) = \frac{x-5}{3}[/tex]
