Suppose that F(t)=-(2t+1)/(t+1). Find a function g so that f(g(t))=t for real numbers t in the domain of g.?

Question

Suppose that F(t)=-(2t+1)/(t+1). Find a function g so that f(g(t))=t for real numbers t in the domain of g.

g(t)=_____

Answer 1

You're basically finding the inverse.

y = -(2t+1)/(t+1)

Switch y and t.

t = -(2y+1)/(y+1)

Solve for y.

t(y+1) = -2y - 1

ty + t = -2y - 1

ty + 2y = -t-1

y(t+2) = -t-1

y = (-t-1)/(t+2)

y = -(t+1)/(t+2)

Then g(t) = -(t+1)/(t+2)