Composite Function Range (Jee Mains)

Functions

Medium

Let f, g: (1, ∞) →

be defined as f(x) = $\frac{{2x + 3}}{{5x + 2}}$ and g(x) = $\frac{{2 - 3x}}{{1 - x}}$ . If the range of the function
fog : [2, 4] →

is [α, β], then $\frac{1}{{\beta - \alpha }}$ is equal to

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