Question

Please help with step by step

Answer 1

$f(x)=10e^{\frac{x-1}{2}}$

substitute f(x) for y
$y=10e^{\frac{x-1}{2}}$

solve for x

$\frac{y}{10}=e^{\frac{x-1}{2}}$

$ln( \frac{y}{10}) = \frac{x-1}{2}$

$2ln( \frac{y}{10})=x-1$

$2ln( \frac{y}{10})+1 =x$

$2ln( \frac{y}{10})$   is esquivent to $2ln(y) - 2ln(10)$

$2ln(y)-2ln(10)+1=x$

Change x to y and y to x

$2ln(x)-2ln(10)+1=y$

Flip formula and substitute y for g(x)

$g(x)=2ln(x)-2ln(10)+1$