Question:

Determine the inverse of the function: ℎ(𝑥) = 2𝑥−3/(1−𝑥)

Solution and steps followed

Answers: f^-1 (x)= x+3

2+x

Work: we replace h(x) with y, y= 2x-3
1-x

We then swap the y for x, x = 2y–3

1-x

Solve for y, x(1–y) = 2y–3

x-xy= 2y–3

2y+xy = x +3. Then factor out y.

y(2+x) =x+3. Divide both sides with 2+x to get

the value of y.

y = x+3

2+x

Finally, we rewrite y as inverse of the function, f^-1 .

f^-1(x) = x+3

2+x