(a) If \(f(x) = \frac{4 - 5x}{2}\), and \(g(x) = x + 6, x \in

Explanation

(a) \(f(x) = \frac{4 - 5x}{2} ; g(x) = x + 6, x \in R\)

Let g(x) = y

\(y = x + 6 \implies x = y - 6\)

Let \(x = g^{-1} (x)\) and y = x.

\(g^{-1}(x) = x - 6\)

\(f \cdot g^{-1}(x) = f(g^{-1}(x))\)

= \(\frac{4 - 5(x - 6)}{2}\)

= \(\frac{4 - 5x + 30}{2}\)

= \(\frac{34 - 5x}{2}\)

(b) \(x = \frac{7 \times 4 - 2(5)}{5 + 4}\)

= \(\frac{18}{9}\)

\(x = 2\)

\(y = \frac{4(-5) + 5(7)}{5 + 4}\)

= \(\frac{15}{9}\)

\((x, y) = (2, 1\frac{2}{3})\)