Question

Find the inverse of the function

y = log₂ (x-3)

Answer 1

h(x)=2^(x-3)

replace h(x) with y:

y=2^(x-3)=(2^x)*(2^-3)=(2^x)/(2^3)=(2^x)/8

y=2^x/8

solve for x:

8y=2^x

log2(8y)=x

Answer 2

`f^(-1)(x)=2^x+3`

Explanation:

Given:

`y=\log_2(x-3)`

To find the inverse of the given function, make x the subject.

`\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b`

`\implies 2^y=x-3`

Add 3 to both sides:

`\implies x=2^y+3`

Swap x for
`f^(-1)(x)` and y for x:

`\implies f^(-1)(x)=2^x+3`