Hello!
To prove that f(x) = 2x - 1 and g(x) = x/2 + 1/2, we can use a composite function. Composite functions are basically (f ∘ g)(x). It combines two functions into one. If they are true inverses, then the answer must be equal to x.
(f ∘ g)(x) = 2(x/2 + 1/2) - 1
(f ∘ g)(x) = x + 1 - 1
(f ∘ g)(x) = x
(g ∘ f)(x) = (2x - 1)/2 + 1/2
(g ∘ f)(x) = x - 1/2 + 1/2
(g ∘ f)(x) = x
Since (g ∘ f)(x) and (f ∘ g)(x) are both equal to x, then the functions of f(x) and g(x) are inverses of each other.
Also, in order for two functions to be inverses, these two functions need to be reflected over the line y = x. In the graph shown below, y = x is in red, y = 2x - 1 is blue, and y = x/2 + 1/2 is green. Looking the graph, you can see they are reflected over the line y = x.
Therefore, the function f(x) = 2x - 1 and g(x) = x/2 + 1/2 are true inverses of each other.
The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share. For example, 12, 20, and 24 have two common factors: 2 and 4. The largest is 4, so we say that the GCF of 12, 20, and 24 is 4. GCF is often used to find common denominators
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Answer:
they are 10km 32 degrees far from each other
Step-by-step explanation:
scott - 100km - 30 degrees
spork - 110km - 62 degrees
how far = difference between them
as spork's distance and degrees are greater than scott we substract Scott's from spork's
110 - 100 = 10 km
62 - 30 = 32 degrees
they are 10km 32 degrees far from each other