**Step 1:**

So, to find the inverse, you basically switch x and y, then solve for y.

j(x) is the same thing as y.

\(y=2x-3\)

Switch the x and y.

\(x=2y-3\)

Solve for y.

Add 3 to both sides.

\(x+3=2y\)

Divide both sides by 2.

\(y=\frac{x+3}{2}\)

Switch the y to j^{-1}(x).

\(j^{-1}(x)=\frac{x+3}{2}\)

__Step 2:__

Now for j(j^{-1}(x)).

You want to plug the value of j^{-1}(x) into j(x) for every x value.

\(j(\frac{x+3}{2})=2(\frac{x+3}{2})-3\)

Multiply the 2.

\(j(j^{-1}(x))=\frac{2(x+3)}{2}-3\)

The 2's cancel.

\(j(j^{-1}(x))=x+3-3\)

The 3's cancel.

\(j(j^{-1}(x))=x\)

__Step 3:__

For j^{-1}(-1), plug -1 in for each x value in j^{-1}(x).

\(j^{-1}(-1)=\frac{(-1)+3}{2}\)

Add -1 and 3.

\(j^{-1}(-1)=\frac{2}{2}\)

2/2 equals 1, so \(j^{-1}(-1)=1\).