(fog)(x) f(x)= x^3; g(x0= 5x^2

Question

(fog)(x) f(x)= x^3; g(x0= 5x^2

Answer 1

Hi Victor,

 

      This question involves composition functions where   (f o g)(x) = f(g(x))

 

For your specific question (f o g)(x)   where f(x)= x^3; g(x)= 5x^2

 

 

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

                                                                                          = f(5x^2)

     substitute 5x^2 in for x in  f(x)= x^3                               = (5x^2)^3

     cube the entire expression                                               = (5^3)(x^2)^3

   simplifying and #using rule of exponents                             = 125x^(2*3)

                                                                                          = 125x^6

 

                    

 

NOTE:  # Here you needed to use the rule of exponents:   (a ^b)^c  =  a^(b*c)

When a base is raise to an exponent is raised to another exponent, the exponents are multiplied.

 

                                       ANSWER:   (f o g)(x) = 125x^6

 

Victor, I hope you have a better understanding of the process for composition functions.

THINK MATH!!