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 $3$ .

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

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

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