a) By addition of functions, we find that h(17) = 28.
b) According to the graph, we find that f(- 1) = 1 and f(e) ≈ - 3.8.
How to analyze functions
In this question we must analyze functions based on properties for operations between functions and representations on Cartesian plane. a) The first part consists in evaluating each of the two functions and find the result by definition of addition between two functions:
f(17) = √(17 - 1)
f(17) = 4
g(17) = 2 · 17 - 10
g(17) = 24
By addition of functions:
h(x) = (f + g) (x) = f(x) + g(x)
h(17) = (f + g) (17) = f(17) + g(17)
h(17) = 4 + 24
h(17) = 28
By addition of functions, we find that h(17) = 28.
b) The second part consists in finding the values corresponding to two points lying on the curve, domain corresponds to horizontal axis and range corresponds to vertical axis:
f(- 1) = 1, f(e) ≈ - 3.8
According to the graph, we find that f(- 1) = 1 and f(e) ≈ - 3.8.
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