test 1

(ii) \( f(x) = \frac{2}{x}, \quad g(x) = 2x^2 - 1 \)

Answer Key:
\( f(x) = \frac{2}{x}, \quad g(x) = 2x^2 - 1 \)

fag = f[g(x)]
\( f(g(x)) = f(2x^2 - 1) \)
\( = \frac{2}{2x^2 - 1} \)

gof = g[f(x)]
\( = g\left(\frac{2}{x}\right) \)
\( = 2\left(\frac{2}{x}\right)^2 - 1 \)
\( = 2 \times \frac{4}{x^2} - 1 \)
\( = \frac{8}{x^2} - 1 \)

\( \text{fog} \ne \text{gof} \)