[tex]f(x)=10e^{\frac{x-1}{2}}[/tex]
substitute f(x) for y
[tex]y=10e^{\frac{x-1}{2}}[/tex]
solve for x
[tex] \frac{y}{10}=e^{\frac{x-1}{2}} [/tex]
[tex]ln( \frac{y}{10}) = \frac{x-1}{2}[/tex]
[tex]2ln( \frac{y}{10})=x-1[/tex]
[tex]2ln( \frac{y}{10})+1 =x[/tex]
[tex]2ln( \frac{y}{10}) [/tex] is esquivent to [tex]2ln(y) - 2ln(10)[/tex]
[tex]2ln(y)-2ln(10)+1=x[/tex]
Change x to y and y to x
[tex]2ln(x)-2ln(10)+1=y[/tex]
Flip formula and substitute y for g(x)
[tex]g(x)=2ln(x)-2ln(10)+1[/tex]
