Let f, g : (1, ∞) → R be defined as f(x) = 2x+3/5x+2 and g(x) = 2-3x/1-x.

Question

Let f, g : \((1, \infty) \rightarrow\) R be defined as f(x) = \(\frac{2x+3}{5x+2}\) and g(x) = \(\frac{2-3x}{1-x}.\) If the range of the function f o g : [2, 4] \(\rightarrow\)  is \([\alpha, \beta],\) then \(\frac{1}{\beta - \alpha}\) is equal to

Answer 1

Answer is: 56 

g(2) = 4 

g(4) = \(\frac{10}{3}\)