Question

Calculate g(b) and (b) where g(x) is the inverse of f() = (2x2 + 5x)1/2 in the domain x > 0, where b= 6. g(b)= (6)=

Answer 1

72 Given f(x) = (a + 5%) Replace f(x) with Y. Y y = (x2+5x) both sides Squaring 42 = oc²+50 and and y X swap x² = y ² - y?+ soep add (9) on both sides 22+ (3?= 42+ sy + (%)? UW dll x² 25 4. (4+ ?) **** 9) = you y et 3 4 2 y=-2 / 2 I D 4x + 25 4 ✓ 40c²tas y = - 2. -57] 4x²4 25 y= 2

as+J4x²+25 J= f*tungo)= -541d42 --5 + 4(6)+25 9 -5+ 169 g(6) = g(6) = 2 -5+ 13 (6) - g → There are two possibilitie Q -5-13 -5+13 6) = g (6)= and 는 2 2 9 ato g (6) = - 4 and g(6) = -1/2 = -9 x AS X x20 gle 6) = = 4 = 4 g (6) g(x)= -5+ V4x2+25 2 2 (8x). g'(x) = 0+ A42√4x²+25 20 g'(x)= + √4x²+25 2 (6) g'(b) = 9' (6) = + ſe(6) ²+ a5 6

13 + 아12 의 g'(6) = + 13 169 AS ozn0 (6) 다 1g 13. g(b (b) = 4 12 'b) : 13