Question

4. Functions f and g are defined for x ER by:
f(x )+ 3x – 1
g: x + 5x – x2
Express gf(x) in the form a – b(x – c)^2 are constants.​

Answer 1

Answer:

$f(x) = 3x - 1 \\ g(x) = 5x - {x}^{2} \\ g{f(x)} = g(3x - 1) \\ = 5(3x - 1) - {(3x - 1)}^{2} \\ = 15x - 3 - {9x}^{2} - 1 + 6x \\ = 21x - {9x}^{2} - 4 \\ = - 9( {x}^{2} - \frac{7}{3} x) - 4 \\ = - 9( {x}^{2} - \frac{7}{3} x + \frac{49}{36} - \frac{49}{36} ) - 4 \\ = - 9 {(x - \frac{7}{6}) }^{2} + \frac{49}{4} - 4 \\ = - 9 {(x - \frac{7}{6}) }^{2} + \frac{33}{4}$

Answer 2

Answer:

this is correct...........................