Question

What is the inverse function of f(x)=5e^x-3+9

Answer 1

Hi,

`f^(-1)(x) = \ln\left((x - 9)/(5)\right) + 3`

Explanation:

To find the inverse function of

`f(x)=5e^((x-3))+9\\`

follow these steps:

• Replace f(x) with y:

`y=5e^((x-3))+9\\`

• Swap the roles of x and y:

`x=5e^((y-3))+9\\`

• Solve for y:
• Subtract 9 from both sides:

`x-9=5e^((y-3))`

• Divide by 5:

`(x-9)/(5) =e^((y-3))`

To isolate y, take the natural logarithm (ln) of both sides:

`ln((x-9)/(5))=y-3`

Now, add 3 to both sides to solve for y:

`y=ln((x-9)/(5))+3`