(remember to show work and explain.)

find the inverse of the functions.

1)

↪y=ln(x-1)

Interchange role of x and y,

↪x=ln (y-1)

Changing it to exponential form,

↪e^x=y-1

↪y=e^x+1

↪inverse of f(x)=y=e^x +1

2)

↪y=ln(2x)

Interchange role of x and y,

↪x=ln(2y)

Changing it to exponential form,

↪e^x=2y

↪y=(e^x)/2=inverse of f(x)

3)

↪y=e^3x

Interchange role of x and y,

↪x=e^3y

Take log on both sides,

↪ln x= ln {(e)^3y}

I have used property of log here to further simplify...

↪ln x= 3y × ln(e)

↪ln x=3y × 1 {as ln e=1}

↪y=ln(x)/3 =inverse of f(x)

bottom left

step-by-step explanation:

the x's and the y's both go up the same amount each time, therefore it will be a linear function because it will go in a straight line when drawn on a graph.

hope this !

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.