Given f(x)=3x^2+2x-10 and g(x)=3x-3 if g(f(x))=2

f(x)=3x^2+2x-10 if x=2

f(x)=3(2)^2+2(2)-10

f(x)=3(4)+2(2)-10

f(x)=12+4-10

f(x)=16-10

f(x)=6

g(x)=3x-3 if g(x)=2

g(x)=3(2)-3

g(x)=6-3 =3

Step-by-step explanation:

f(x)

g(x)

5/3 and -7/3

Step-by-step explanation:

Given f(x)=3x²+2x-10 and g(x)=3x-3

g(f(x))=2 :    g(3x²+2x-10) =2

replace  x  with : 3x²+2x-10  in g(x)

3( 3x²+2x-10)-3 =2

9x²+6x -35 =0

the discriminant  delta = b² - 4ac    a = 9   and b=6 and c = -35

delta = 6² - 4(9)(-35) = 1296 = 36²

x1 = (-6+36)/18 = 30/18 = 5/3

x2 = (-6-36)18= -42/18 = -7/3

a - base

b - exponent

so,