Question

The red is not the answer. I can’t figure it out

Answer 1

Given:

`f(x)=(1)/(4x+10)`

Required:

To find the inverse of a givne function.

Step-by-step explanation:

Consider the given function

`f(x)=(1)/(4x+10)`
`y=(1)/(4x+10)`

Swap x and y, we get

`x=(1)/(4y+10)`

Now solve for y.

`\begin{gathered} 4y+10=(1)/(x) \\ \\ 4y=(1)/(x)-10 \\ \\ y=(1)/(4x)-(10)/(4) \\ \\ y=(1)/(4x)-(5)/(2) \end{gathered}`

Now

`\begin{gathered} f^(-1)(x)=(1)/(4x)-(5)/(2) \\ \\ =(1-10x)/(4x) \end{gathered}`

Final Answer:

`f^(-1)(x)=(1)/(4x)-(5)/(2)`