Question

Find the inverse of the function below f(x)=2^x+6

Answer 1

`Solution, \mathrm{Inverse\:of}\:2^x+6:\quad (\ln \left(x-6\right))/(\ln \left(2\right))`

`Steps:`

Definition
`If\;a\;function\;f\left(x\right)\;s\;mapping\;x\;to\;y,\;then\;the\;inverse\;function\;of\;f\left(x\right)\;maps\;y\;back\;to\;x.`

`y=2^x+6`

`\mathrm{Interchange\:the\:variables}\:x\:\mathrm{and}\:y, x=2^y+6`

`\mathrm{Solve}\:x=2^y+6\:\mathrm{for}\:y, y=(\ln \left(x-6\right))/(\ln \left(2\right)), (\ln \left(x-6\right))/(\ln \left(2\right))`

The correct answer is
`(\ln \left(x-6\right))/(\ln \left(2\right))`

Hope this helps!!!

<3 -austint1414