Question 1

If f(x)=x-3/x, g(x)=x+3, and h(x)=2x+1, what is (g o h o f)(x)?

Question 2

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.

Question 3

Answer:

(gohof)(x)=2x-(6)/(x)+4

Explanation:

We need to find out
(gohof)(x)

Given:-
$f(x)=x-(3)/(x), \ g(x)=x+3 \ \text{and} \ h(x)=2x+1$

First we calculate
(hof)(x)

(hof)(x)=h(f(x))

(hof)(x)=2x+1

(hof)(x)=2(x-(3)/(x))+1

(hof)(x)=2x-(6)/(x)+1

Now,Put (hof)(x) in g(x)

(gohof)(x)=g(h(f(x)))

(gohof)(x)=g((hof)(x))

(gohof)(x)=2x-(6)/(x)+1+3

(gohof)(x)=2x-(6)/(x)+4

Therefore,
(gohof)(x)=2x-(6)/(x)+4

Arno Hilke · Answer 1 · 2019-06-12T19:19:47+0000

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.

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