Find all values of x satisfying the given conditions fx 2x

Find all values of x satisfying the given conditions. f(x) = 2x - 3, g(x) = x^2 - 6x + 18, and (f o g)(x) = 17 The values of x satisfying the given conditions are. (Use a comma to separate answers as needed.)

Solution

f(x)=2x-3 , g(x)=x²-6x+18

(fog)(x)=17

f(g(x))=17

f(x²-6x+18)=17

2(x²-6x+18)-3=17

2x²-12x+36-3-17=0

2x²-12x +16=0

x²-6x+8=0

(x-4)(x-2)=0

x=4,2