Question

4. I need help with question in the attached picture!

Answer 1

Option D is correct.

Explanation:

`f(x)= (2x+1)/(x-4) \,\,find \,\,value\,\,of\,\, f^(-1)(3)`

We know that f(a) =b ⇔ f^-1 (b) =a

Using this,

We are given
`f^(-1)(3)=x => f(x)=3`

and
`f(x)= (2x+2)/(x-4)`

putting value of f(x)

`3= (2x+1)/(x-4)\\3(x-4) = 2x+1\\3x-12 = 2x+1\\Adding\,\,like\,\,terms\,\,\\3x-2x = 12+1\\x=13\\So, f^(-1)(3) = 13`

Option D is correct.

Answer 2

D. 13

EXPLANATION

We have

`f(x) = (2x + 1)/(x - 4)`

To find

`{f}^( - 1) (3)`

means we want to find an x-value whose image is 3.

`(2x + 1)/(x - 4) = 3`

We cross multiply,

`2x + 1 = 3(x - 4)`

Expand:

`2x + 1 = 3x - 12`

Combine like terms,

`3x - 2x = 12 + 1`

`x = 13`

`\therefore{f}^( - 1) (3)= 13`