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12345 [234]
3 years ago
12

If f (x) = StartRoot x minus 3 EndRoot, which inequality can be used to find the domain of f(x)? Options Below

Mathematics
2 answers:
Aleksandr [31]3 years ago
8 0

The inequality x-3 \geq 0  can be used to find the domain of f(x)=\sqrt{x-3}

Answer: Option B

<u>Step-by-step explanation:</u>

We have f(x)=\sqrt{x-3}, domain is the set of all possible x-values which will make the function "work", and will output real y-values. Basically to find domain of any function means to find range of values of x that will give real values of y.

For the equation  f(x)=\sqrt{x-3} , we know that there's no value  ( iota or complex numbers are there but here we will deal with real numbers ) of negative numbers under square root  

∴{(} x-3 {)} must be greater than or equal to 0.

⇒ x-3 \geq 0

umka2103 [35]3 years ago
6 0

Answer:

B

Step-by-step explanation:

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The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)).

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<h3>What is composition function?</h3>

The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)). In this operation, the function g exists used for the outcome of applying the function f to x.

Given:

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a) (f o g)(x) = f[g(x)]

f[g(x)] = 4(x² - 3)² + 1

substitute the value of g(x) in the above equation, and we get

    = 4(x⁴ - 24x + 9) + 1

simplifying the above equation

    = 4x⁴ - 96x + 36 + 1

    = 4x⁴ - 96x + 37

(f o g)(x) = 4x⁴ - 96x + 37

b) (g o f)(x) = g[f(x)]

substitute the value of g(x) in the above equation, and we get

g[f(x)] = (4x² + 1)²- 3

      = 16x⁴ + 8x² + 1 - 3

simplifying the above equation

      = 16x⁴ + 8x² - 2

(g o f)(x) = 16x⁴ + 8x² - 2.

Therefore, the correct answer is (f o g)(x) = 4x⁴ - 96x + 37 and

(g o f)(x) = 16x⁴ + 8x² - 2.

To learn more about the function refer to:

brainly.com/question/26709985

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