Question

10.
Iff: R → R and g: R → R are defined by f(x) = x² - 2x + 1 and g(x) = 3x - 1,
x € R. Find (i) fog(x) (ii) gof(x) (iii) f'(x).​

Answer 1

Step-by-step explanation:

$fog(x) = f(g(x)) = f(3x - 1) \\ = {(3x - 1)}^{2 }-2(3x-1)+1 \\ = 9 {x}^{2}-6x + 1 - 6x + 2 + 1 \\ = 9 {x}^{2} - 12x + 4 \\ similarly \\ gof(x) = g(f(x)) = \\ g( {x}^{2} - 2x + 1) \\ = 3( {x}^{2} - 2x + 1) + 1 \\ = 6 {x}^{2} - 6x + 2$