(a) If (f(x) = frac{4 – 5x}{2}), and (g(x) = x + 6, x in R), find (f circ g^{-1}).
(b) P(x, y) divides the line joining (7, -5) and (-2, 7) internally in 5 : 4. Find the coordinates of P.
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, 1frac{2}{3}))