Given #f(x)=3x^4-2x^2# & #g(x)= 2/sqrtx, (x ≠0)# how do you find the composition of f and g?

1 Answer
Feb 2, 2018

See explanation.

Explanation:

There are two ways of composing 2 functions:

  • #f(g(x))#

To find this composition you have towrite the formula of #g(x)# for every #x# in the formula of #f#. Here we get:

#f(g(x))=3*g^4(x)-2*g^2(x)#

#f(g(x))=3*(2/sqrt(x))^4-2*(2/sqrt(x))^2#

#f(g(x))=3*16/x^2-2*4/x=48/x^2-8/x=(8*(6-x))/(x^2)#

  • #g(f(x))#

To find this composition you have towrite the formula of #f(x)# everywhere #x# is in the formula of #g#. Here we get:

#g(f(x))=2/(sqrt(f(x)))=2/sqrt(3x^4+2x^2)#