Discrete mathematics

Question

Given the following functions f(x) = 5x² - 3x +20 and g(x) = 2x +3, Find f^-1(g(x))

Answer 1

f(x) = 5x^2 -3x +20

y=5x^2 -3x +20 switch x and y to find the inverse

x = 5y^2 -3y +20

solve for y

5y^2 -3y +20-x = 0 use the quadratic formula

y= 3/10 + or - (1/10)sqr(9-4(5)(20-x)) =

= (3-sqr(-391+4x)/10 or (3+sqr(-391+4x)/10

f^-1(x) = (3+sqr(391+4x)/10 replace x by g(x)

f^-1(g(x)) = (3+sqr(391+4(2x+3))/10

= (3+sqr(403+8x))/10