Theory question 101
Functions(a) If f(x) = (4 − 5x)/2 and g(x) = x + 6, x ∈ R, find f o g−1
(b) P(x, y) divides the line joining (7, −5) and (−2, 7) internally in the ratio 5:4. Find the coordinates of P.
Show the model answer
Model answer
(a) g⁻¹(x) = x − 6. f(g⁻¹(x)) = (4 − 5(x − 6))/2 = (34 − 5x)/2.
(b) x = (5(−2) + 4(7))/9 = 2; y = (5(7) + 4(−5))/9 = 5/3. P(2, 5/3).
Explanation
For internal division in m : n use (mx₂ + nx₁)/(m + n).