Question

For a given function, f of x, the inverse is denoted by f inverse of x.



If f of x equals StartFraction 2 x plus 5 over 3 x EndFraction, what is f inverse of x?

Answer options with 5 options
A.
StartFraction 5 over 3 x minus 2 EndFraction

B.
StartFraction 3 x over 2 x plus 5 EndFraction

C.
negative StartFraction 2 x plus 5 over 3 x EndFraction

D.
StartFraction negative 3 x over 2 x plus 5 EndFraction

E.
StartFraction 3 x minus 2 over 5 EndFraction

Answer 1

Let y = (2x+5)/(3x). Solve for x:

y(3x) = 2x + 5 → 3yx - 2x = 5 → x(3y - 2) = 5 → x = 5/(3y - 2).

Thus f⁻¹(x) = 5/(3x - 2), which is option A.