Question

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

Answer 1

5/3 and -7/3

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

Answer 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

Explanation:

f(x)

1. replace x by 2
2. do exponent
3. distribute the brackets
4. do addition and subtraction

g(x)

1. replace x by 2
2. distribute the bracket
3. do subtraction