Question

f(x)=1÷2x+1 find f(f(x))

Answer 1

Johnson Z.

May 14, 2016

Answer:

f−1(x)=−x+12−xyes, it is a function

Explanation:

Determining the Inverse Function
Given,

f(x)=2x−1x−1

Substitute y for f(x).

y=2x−1x−1

Swap the x and y.

x=2y−1y−1

Solve for y.

x(y−1)=2y−1

xy−x=2y−1

2y−xy=−x+1

Factor out y from the left side.

y(2−x)=−x+1

y=−x+12−x

Rewrite y as f−1(x).

∣∣ ∣ ∣∣¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯aaf−1(x)=−x+12−xaa∣∣∣−−−−−−−−−−−−−−−−−−−−−