Question

Find a formula for the inverse of the function:

f(x) = e^(2x-1)

e is all raised to (2x-1)

Answer 1

Let\[y=e^{2x}-1\]\[y+1=e^{2x}\]\[ln(y+1)=ln(e^{2x})= 2x\]\[x=\frac{1}{2}ln(y+1)\]meaning that if you supply the y value I can give the x-value that mapped to it under the original function. NB beware domain and range issues.