Calculate ??( hofog)x if h(x) = 3x , g = 1/3x and f =2x+5

1 Answer
May 8, 2018

(h@f@g)(x)=2x+15(hfg)(x)=2x+15

Explanation:

(h@f@g)(x)(hfg)(x) is known as a composite function. Here's how composite functions work:

let's say that x=1x=1. Your function g(x) = 1/3(x)g(x)=13(x) now produces a yy output of 1/313 , since g(1)=1/3(1)g(1)=13(1). Within a composite function, the y-value of one function becomes the x-value of the next, like so:

g(1)=1/3=>f(1/3)=17/3=>h(17/3)=17g(1)=13f(13)=173h(173)=17

Therefore,
(h@f@g)(1)=17(hfg)(1)=17

Based on this, to find the function for (h@f@g)(x)(hfg)(x) (combined from right to left, by the way), simply replace xx in f(x)f(x) with the function g(x)g(x), and replace xx in h(x)h(x) with the function of (f@g)(x)(fg)(x), to get (h@f@g)(x)(hfg)(x).

This, simplified, is equal to 2x+152x+15, and therefore (h@f@g)(1)=2(1)+15=17(hfg)(1)=2(1)+15=17

Hope that helps!