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<em>A function f (x) and g (x) then:</em>
<em>(f + g) (x) = x² - x + 6</em>
<em>Further explanation</em>
Like the number operations we do in real numbers, operations such as addition, installation, division or multiplication can also be done on two functions.
Suppose a function f (x) and g (x) then:
(f + g) (x) = f (x) + g (x)
(f + g) (x) is a new function of the sum of f (x) and g (x)
Likewise with other function operations:
(f-g) (x) = f (x) - g (x)
(fg) (x) = f (x) x g (x)
(f / g) (x) = f (x) / g (x)
In addition to the above operations we can combine two functions using the function composition with the symbol o
(fog) (x) = f ((g (x))
Known on the question
f (x) = x² + 1
g (x) = 5 x
Summing the two functions f (x) and g (x):
(f + g) (x) = f (x) + g (x)
(f + g) (x) = x² + 1 + 5 - x
(f + g) (x) = x² - x + 6
<h3><em>Learn more</em></h3>F (x) and g (x) functions
function h (x) = f (x) ∘ g (x)
Find the function rule for g (x)
Keywords: f (x) and g (x) functions, function operations, addition, subtraction, division, multiplication
No product results in -1, hence δlmn is NOT a right triangle showing that lydia's assertion is incorrect
<h3>Perpendicular lines</h3>In order to determine whether triangle lmn is right-angled, we need to determine the slope of lm, ln, and mn first as shown:
For the slope of lm:
For the slope of ln:
For the slope of mn:
- If any of the two lines is perpendicular, hence the triangle lmn is right-angled.
- To check, we will take the product of the slopes and see if it is equivalent to -1.
Product of slope lm and ln
Since no product results in -1, hence δlmn is NOT a right triangle showing that Lydia's assertion is incorrect
Learn more on slopes here: brainly.com/question/3493733