SOLUTION: if f(x)=3x-4 and g(x)=x³, evaluate f<font face = "bookshelf symbol 7">g</font>g and g<font face = "bookshelf symbol 7">g</font>f.

Algebra ->  College  -> Linear Algebra -> SOLUTION: if f(x)=3x-4 and g(x)=x³, evaluate f<font face = "bookshelf symbol 7">g</font>g and g<font face = "bookshelf symbol 7">g</font>f.      Log On


   

Question 111791: if f(x)=3x-4 and g(x)=x³, evaluate fgg and ggf.
Answer by Edwin McCravy(20063) About Me  (Show Source):
You can put this solution on YOUR website!
 
if f(x)=3x-4 and g(x)=x³, evaluate fgg and ggf.

fgg(x) means to replace ONLY the x's in the right side of 
the equation for f(x) by the ENTIRE RIGHT SIDE of 
the equation for g(x).

ggf(x) means to replace ONLY the x's in the right side of 
the equation for g(x) by the ENTIRE RIGHT SIDE of 
the equation for f(x).


To find fgg(x), we start with the right side of 
equation for f(x), which is:

           3x - 4

and the right side of g(x), which is

             x³

Now we replace ONLY the x in 3x - 4 by the ENTIRE x³

So we end up with

         3x³ - 4

So fgg = 3x³ - 4

-----------------------

To find ggf(x), we start with the right side of 
the equation for g(x), which is:

           x³

and the right side of f(x), which is

          3x - 4

Now we replace ONLY the x in x³ by the ENTIRE 3x - 4

So we end up with

         (3x - 4)³

So ggf = (3x - 4)³.

Edwin