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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
The sum of the two numbers is equal to 70.
- Let the first number be x.
- Let the second number be y.
In this exercise, you're required to find two numbers by translating the word problem into an algebraic expression and then solving for the unknown variables (x and y).
Translating the word problem into an algebraic expression, we have;
Two numbers differ by 8:
....equation 1.
The product of the two numbers is 713:
....equation 2.
To calculate the sum of the two numbers:
First of all, we would solve for each of the unknown variables (x and y).
From eqn. 1, we have:
....equation 3.
Substituting eqn. 3 into eqn. 2, we have:
Solving the quadratic equation by factorization, we have:
y = -23 or 31.
For the value of x, when y = 31:
x = 39
Now, we can calculate the sum of the two numbers:
Read more on word problems here: brainly.com/question/13170908