Question

Please help me solve this problem step by step. I don’t get it

Answer 1

Part a

we have the function

`f(t)=\log_2(t)`

Find out the inverse

step 1

Let

y=f(t)

step 2

Exchange the variables (y for t and t for y)

`t=\log_2y`

step 3

Isolate the variable y

Apply the definition of logarithm

`\begin{gathered} 2^t=y \\ y=2^t \\ f^(-1)(t)=2^t \end{gathered}`

Part B

we have the function

`g(t)=(1)/(t-2)`

Find out the inverse of function g(t)

`y=(1)/(t-2)`

Exchange the variables

`t=(1)/(y-2)`

Isolate the variable y

`\begin{gathered} t(y-2)=1 \\ y-2=(1)/(t) \\ y=(1)/(t)+2 \\ \\ g^(-1)(t)=(1)/(t)+2 \end{gathered}`

The domain of the inverse function is all real numbers except for t=0

so

interval (-infinite,0) U (0, infinite)