Question

MULTIPLE CHOICE Choose the one alternative that best completes the statement or answers the question.

For the given functions f and g, find the requested composite function value f(x) = g(x) = x² + 9; Find (g ∘ f)(-2) A) 145 B) 25 C) 13
For the given functions f and g, find the requested composite function. f(x) = √(x + 10), g(x) = 8x - 14; Find (f - g)(x) A) √(2x - 10) B) √(x+ 10 - 14) C) √(2x - 4) D) √(x - 4)

Answer 1

The composite function (g ∘ f)(-2) equals 178, which is not among the provided options, potentially due to an error in the question. Similarly, for the function operation (f - g)(x), the result is √(x + 10) - 8x + 14, which does not match the given choices, suggesting a possible mistake in the question or choices.

Step-by-step explanation:

The mathematics question asks for the computation of composite functions and function operations for given functions f(x) and g(x). In the first part of the question, we are given f(x) = g(x) = x² + 9 and asked to find (g ∘ f)(-2). To find this, we first compute f(-2), and then use that result as the input for g.

f(-2) = (-2)² + 9 = 4 + 9 = 13
g(f(-2)) = g(13) = 13² + 9 = 169 + 9 = 178

So the answer is not listed in the provided choices, indicating there may be a typo or mistake in the question.

In the second part, we are asked to find (f - g)(x) with f(x) = √(x + 10) and g(x) = 8x - 14. The operation (f - g)(x) implies subtracting g(x) from f(x). Therefore:

(f - g)(x) = √(x + 10) - (8x - 14) = √(x + 10) - 8x + 14
This expression does not match any of the provided choices, indicating there may be an error in the question or the choices provided.

Answer 2

The composite function (g ∘ f)(-2) equals 178, which is not among the provided options, potentially due to an error in the question. Similarly, for the function operation (f - g)(x), the result is √(x + 10) - 8x + 14, which does not match the given choices, suggesting a possible mistake in the question or choices.

Step-by-step explanation:

The mathematics question asks for the computation of composite functions and function operations for given functions f(x) and g(x). In the first part of the question, we are given f(x) = g(x) = x² + 9 and asked to find (g ∘ f)(-2). To find this, we first compute f(-2), and then use that result as the input for g.

f(-2) = (-2)² + 9 = 4 + 9 = 13
g(f(-2)) = g(13) = 13² + 9 = 169 + 9 = 178

So the answer is not listed in the provided choices, indicating there may be a typo or mistake in the question.

In the second part, we are asked to find (f - g)(x) with f(x) = √(x + 10) and g(x) = 8x - 14. The operation (f - g)(x) implies subtracting g(x) from f(x). Therefore:

(f - g)(x) = √(x + 10) - (8x - 14) = √(x + 10) - 8x + 14
This expression does not match any of the provided choices, indicating there may be an error in the question or the choices provided.

Answer 3

The composite function (g ∘ f)(-2) equals 178, which is not among the provided options, potentially due to an error in the question. Similarly, for the function operation (f - g)(x), the result is √(x + 10) - 8x + 14, which does not match the given choices, suggesting a possible mistake in the question or choices.

Step-by-step explanation:

The mathematics question asks for the computation of composite functions and function operations for given functions f(x) and g(x). In the first part of the question, we are given f(x) = g(x) = x² + 9 and asked to find (g ∘ f)(-2). To find this, we first compute f(-2), and then use that result as the input for g.

f(-2) = (-2)² + 9 = 4 + 9 = 13
g(f(-2)) = g(13) = 13² + 9 = 169 + 9 = 178

So the answer is not listed in the provided choices, indicating there may be a typo or mistake in the question.

In the second part, we are asked to find (f - g)(x) with f(x) = √(x + 10) and g(x) = 8x - 14. The operation (f - g)(x) implies subtracting g(x) from f(x). Therefore:

(f - g)(x) = √(x + 10) - (8x - 14) = √(x + 10) - 8x + 14
This expression does not match any of the provided choices, indicating there may be an error in the question or the choices provided.