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Ronch [10]
3 years ago
11

Find the domain and range for the following functions:

Mathematics
1 answer:
Andreyy893 years ago
4 0

Answer with Step-by-step explanation:

Since we have given that

a. f: ℝ → ℝ given by f(x) = x + 2

Domain would be all real numbers i.e. (-∞, ∞)

Range would be all real numbers i.e. (-∞, ∞)

b. g: ℝ → ℝ given by g(x) = √x − 1

Domain would be all positive numbers i.e. [0,∞)

Range would be [-1,∞)

c. f(g(x))

f(g(x))=f(\sqrt{x}+1)=\sqrt{x}+1+2=\sqrt{x}+3

Domain would be  [0,∞)

Range would be [3,∞)

d. g(f(x))

g(x+2)=\sqrt{x+2}-1

Domain would be [-2,∞)

Range would be (0,∞)

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A quadratic equation is a polynomial of degree two. A quadratic equation is in the form:

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Quadratic equation can be solved using different methods, such as completing the square method, quadratic formula.

Solving the equation 2x² - 10x - 20 = 8 using completing the square:

2x² - 10x - 20 = 8

2x² - 10x = 28

Divide through by 2, to make the coefficient of x² to be 1:

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Add to both sides, the square of half of the coefficient of x [i.e. (-5/2)² = 6.25]

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taking square root of both sides:

x - 2.5 = √20.25

x - 2.5 = ±4.5

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3 years ago
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