algebra help

Question

f(x)=x+2 g(x)=4x^2-10

(FoG)(x)

(GoF)(x)

Answer 1

To solve (FoG)(x), everywhere you see the value x in the function f(x) substitute the value of g(x) [in this case, 4x²-10], so in this case:

 

(FoG)(x) = (4x²-10)+2

             =   4x²-10+2

             =   4x²-8

 

Likewise, to solve (GoF)(x), everywhere you see the value x in the function g(x) substitute the value of f(x) [in this case, x+2], so in this case:

(GoF)(x) = 4(x+2)²-10
             = 4(x²+4x+4)-10
             = 4x²+16x+6

Answer 2

f(x)=x+2   g(x)=4x²-10
Find (FoG)(x) and (GoF)(x)

 

The notation (fog)(x) refers to a composite function.  Basically, you just replace the x in f(x) with g(x)

 

(fog)(x) = (4x²-10)+2 = 4x²-8                 Replace the x+2 with g(x)+2

 

(gof)(x) = 4(x+2)²-10 = 4x²+16x+6        Replace the x in 4x²-10 with with 4(f(x))²-10

Answer 3

(f o g)(x)=f(g(x))

             = f(4x^2-10)

             = (4x^2 - 10) + 2 

             = 4x^2 -8

 

(g o f)(x) = g(f(x))

              = g(x+2)

              = 4(x+2)^2 - 10

              = 4(x^2+4x+4) - 10

              = 4x^2 + 16x + 16 - 10

              = 4x^2 + 16x + 6