Given the functions f(x) = 2x -1 and g(x) =

1 answer:

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Answer:

Please check the explanation.

Step-by-step explanation:

Given

f(x) + g(x) = (2x - 1) + (2 - x)

= 2x -1 + 2 - x

= x + 1

f(x) - g(x) = (2x - 1) - (2 - x)

= 2x - 1 - 2 + x

= 3x - 3

g(-5) - f(-5)

Putting x = -5 in g(x) = 2 - x

g(x) = 2 - x

g(-5) = 2 - (-5) = 2+5 = 7

Putting x = -5 in f(x) = 2x - 1

f(x) = 2x - 1

f(-5) = 2(-5) - 1

= -10 - 1

= -11

Thus,

g(-5) - f(-5) = 7 - (-11) = 7+11 = 18

f(x).g(x) = (2x - 1) (2 - x) = -2x² + 5x - 2

f(g(x)) = f(2-x)

= 2(2-x)-1

= 4-2x-1

= 3-2x

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bekas [8.4K]

Using the concept of domain, the domain of (f.g)(x) is given by:

{x ∈ ℝ | x ≠ 3}

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The domain of a function is given by all possible input values, that is, <u>on a graph, all values that the x-axis assumes.</u>
In the graph, <u>function f assumes all real values.</u>
Function g is not defined for x = 3, thus, it's domain is all real values except 3.
Thus, the multiplication, as $fg(x) = f(x) \times g(x)$ , will also not be defined at x = 3, and the domain of the multiplication is: