So, (g o h o f)(x) = g((hof)(x));
But, (hof)(x) = h(f(x)) = 2·f(x) + 1 = 2·( x - 3/x) + 1 = 2x - 6/x + 1;
Then, g(2x - 6/x + 1) = 2x - 6/x + 1 + 3 = 2x -6/x + 4.
Answer:
[tex](gohof)(x)=2x-\frac{6}{x}+4[/tex]
Step-by-step explanation:
We need to find out [tex](gohof)(x)[/tex]
Given:- [tex]f(x)=x-\frac{3}{x}, \ g(x)=x+3 \ \text{and} \ h(x)=2x+1[/tex]
First we calculate [tex](hof)(x)[/tex]
[tex](hof)(x)=h(f(x))[/tex]
[tex](hof)(x)=2x+1[/tex]
[tex](hof)(x)=2(x-\frac{3}{x})+1[/tex]
[tex](hof)(x)=2x-\frac{6}{x}+1[/tex]
Now,Put (hof)(x) in g(x)
[tex](gohof)(x)=g(h(f(x)))[/tex]
[tex](gohof)(x)=g((hof)(x))[/tex]
[tex](gohof)(x)=2x-\frac{6}{x}+1+3[/tex]
[tex](gohof)(x)=2x-\frac{6}{x}+4[/tex]
Therefore, [tex](gohof)(x)=2x-\frac{6}{x}+4[/tex]
