Question

Please help with step by step

Answer 1

`f(x)=10e^{(x-1)/(2)}`

substitute f(x) for y

`y=10e^{(x-1)/(2)}`

solve for x


`(y)/(10)=e^{(x-1)/(2)}`


`ln( (y)/(10)) = (x-1)/(2)`


`2ln( (y)/(10))=x-1`


`2ln( (y)/(10))+1 =x`


`2ln( (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`