How do you find the compositions given #f(x) = x+4/3 # and #g(x) = 3x-4#?

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Answer 1 · 2015-11-30T22:36:33

#{((f@g)(x)=3x-8/3),((g@f)(x)=3x):}#

Composition functions are when you take one function and plug the entire function into another function.

For example, if we wanted to calculate #(f@g)(x)#, we would take #g(x)#, which is #3x-4#, and plug it in for the #x# in #f(x)#.

Let's try:

If #f(x)=x+4/3#:
#(f@g)(x)=overbrace((3x-4))^("x replaced by g(x)")+4/3#

We can simplify this by adding #-4# and #4/3#.

#(f@g)(x)=3x-8/3#

We can do the same process, just switching which function is plugged into which, to find #(g@f)(x)#.

If #g(x)=3x-4#:
#(g@f)(x)=3overbrace((x+4/3))^("x replaced by f(x)")-4#

Distribute the #3#.

#(g@f)(x)=3x+4-4#

#(g@f)(x)=3x#