Question

If $f(x) = \frac{4x + 5}{6x - 4}, \, x \neq \frac{2}{3}$ and $(fof)(x) = g(x)$, where g : \mathbb{R} - \left\\{ \frac{2}{3} \right\\} \rightarrow \mathbb{R} - \left\\{ \frac{2}{3} \right\\}, then $(gogogog)(4)$ is equal to

• A. $-\frac{19}{20}$
• B. $\frac{19}{20}$
• C. $-4$
• D. 4

Answer 1

Answer: (D)

4

Answer 2

Given:

$f(x) = \frac{4x + 3}{6x - 4}$

Compute $g(x)$ as:

$g\left(\frac{4x + 3}{6x - 4}\right) = \frac{\left(\frac{4x + 3}{6x - 4}\right) + 3}{\left(\frac{4x + 3}{6x - 4}\right) - 4} = \frac{34x}{34} = x$

Thus:

$g(x) = x \quad \implies \quad g(g(g(4))) = 4$