Question

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

Answer 1

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.

Answer 2

x = 5

equate f(x) = $\frac{25}{9}$

$\frac{4x + 5}{x + 4}$ = $\frac{25}{9}$ → (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 = $\frac{55}{11}$ = 5