17)If \(f(x) = x^2 - 1\), \(g(x) = x - 2\) find a, if \(g \circ f(a) = 1\).

17)If \(f(x) = x^2 - 1\), \(g(x) = x - 2\) find a, if \(g \circ f(a) = 1\).

Answer: \(f(x) = x^2 - 1\), \(g(x) = x - 2\)

\(f(a) = a^2 - 1\)

Given, \((g \circ f)(a) = 1\)

\(g[f(a)] = 1\)

\(g[a^2 - 1] = 1\)

\((a^2 - 1) - 2 = 1\)

\(a^2 - 3 = 1\)

\(a^2 = 1 + 3 = 4\)

\(a = \pm 2\)