Answer:
[tex]f^{-1}(x)=\frac{3}{5}x+\frac{28}{5}[/tex]
Explanation:
The given equation is
[tex]5x - 17 = 11 + 3y[/tex]
We need to find the inverse of the function.
Step 1: Interchange x and y.
[tex]5y - 17 = 11 + 3x[/tex]
Step 2: Isolate y on left side.
Add 17 on both sides.
[tex]5y - 17+17= 11 + 3x+17[/tex]
[tex]5y=3x+28[/tex]
Divide both sides by 5.
[tex]y=\frac{3x+28}{5}[/tex]
[tex]y=\frac{3}{5}x+\frac{28}{5}[/tex]
Step 3: Substitute [tex]y=f^{-1}(x)[/tex].
[tex]f^{-1}(x)=\frac{3}{5}x+\frac{28}{5}[/tex]
Therefore, the inverse of the function is [tex]f^{-1}(x)=\frac{3}{5}x+\frac{28}{5}[/tex].
