Question

What element in domain ha image 25/9 under function f(x)= 4x+5/x+4

Answer 1

x = 5

equate f(x) =
`(25)/(9)`

`(4x + 5)/(x + 4)` =
`(25)/(9)` → (cross- multiply)

9(4x + 5) = 25(x + 4) → (distribute both sides )

36x + 45 = 25x + 100 → ( subtract 25x from both sides )

11x + 45 = 100 → ( subtract 45 from both sides )

11x = 55 → ( divide both sides by 11 )

x =
`(55)/(11)` = 5

Answer 2

First I'll make the assumption that you mean

4x+5

f(x) = ------------

x+4

and then set this function = to 25/9:

4x+5 25

f(x) = ------------ = ------

x+4 9

Solve for x: Cross-multiplying, we get 36x + 45 = 25x + 100.

Consolidating like terms, we get 11x = 55. Thus, x = 5.