For the functions f(x) = 2x − 6 and g(x) = 5x + 1, which composition produces the greatest output? both compositions produce the same result. no composition produces output. f(g(x)) produces the largest output. g(f(x)) produces the largest output.

**Answer 1**

g(f(x)) = 5(2x-6)+1 = 10x-30+1 = 10-29 10x-4>10-29 because from f(g(x)) you subtract less amount. The answer to your question is C. I hope this is the answer you were looking for and that it helped you.

**answer 2**

. You can see that the graph of g(f(x)) is below the graph of f(g(x)), so the composite f(g(x)) produces the highest output.

**answer 3**

f(g(x)) produces the largest output. g(f(x)) produces the largest output.

**answer 4**

So f(x)=2x-6 and g(x)=5x+1. First I’m going to do of(g(x)), which is f(g(x))=2(5x+1)-6 => f(g(x))=10x+2-6 => f(g(x))=10x-4. And g(f(x))=5(2x-6)+1 => g(f(x))=10x-30+1 => g(f(x))=10x-29. Both have the same slope, but f(g(x)) has a larger intercept, making it greater than g(f(x)). For example, let x=1, then f(g(x))=10x-4 => f(g(x))=10(1)-4 => f(g(x))=10-4 = > f(g(x))=6, and g(f(x))=10x-29 => g(f(x))=10(1)-29 => g(f(x))=10 – 29 => g(f(x))=-19, and 6 is greater than -19, so f(g(x)) is greater than g(f(x)). Hope this helps and fixes my error.

**Answer 6**

What is the solution ?

**Answer 7**

1) The composition of functions consists in applying a function to the result of another. 2) f(x) composed of g(x) is (f ° g) (x) = f [ g(x) ] means to apply the function f to the result of g(x). 3) g(x) composed of f(x) is (g ° f) (x) = g [ f(x) ] means to apply the function g to the result of f(x). 4) Do both: i) f (g(x) = 2 [ g(x) ] – 6 = 2 [ 5x + 1] – 6 = 10x + 2 – 6 = 10x – 4 ii) g (f(x) = 5 [ 2 (2x – 6) ] + 1 = 5 [ 4x – 12] + 1 = 20x – 60 5) Compare the two outputs: 20x – 60 > 10x – 4? Solve the inequality: 20x – 10x > 60 – 4 ⇒ 10x > 56 ⇒ x > 5.6 Then: i) for x = 5.6 the two outputs are equalii) for x > 5.6 g(f(x) is majoriii) for x < 5.6 f (x) is major.

**Answer 8**

Remember that to solve something like f(g(x)), we take the value assigned to x, solve for g(x), and take the output for g(x) and put it into f(x). By inserting the value of 1 into x, we can see that f(g(x)) will create the largest output. As g(f(x)) will leave us -19, while f(g(x)) will leave us 6.