Which property justifies the following

Drag the expressions to the correct functions. Not all expressions will be used.

postnew [5]

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)).

Let the functions be f(x) = 4x² + 1 and g(x) = x² - 3

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

(g o f)(x) = 16x⁴ + 8x² - 2.

<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:

f(x) = 4x² + 1 and g(x) = x² - 3

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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7 0

2 years ago

ULLIVLY/1/2/3/assessment

zvonat [6]

<h3>The worth after 4 years is $ 680.24</h3>

<em><u>Solution:</u></em>

<em><u>The formula for compound interest, including principal sum, is:</u></em>

$A = p(1+\frac{r}{n})^{nt}$

Where,

A = the future value of the investment

P = the principal investment amount

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per unit t

t = the time the money is invested

From given,

n = 1 ( since interest is compounded annually)

p = 500

t = 4

$r = 8 \% = \frac{8}{100} = 0.08$

<em><u>Substituting the values we get,</u></em>

$A = 500(1+ \frac{0.08}{1})^{1 \times 4}\\\\A = 500(1.08)^4\\\\A = 500 \times 1.36048896\\\\A = 680.24448 \approx 680.24$

Thus the worth after 4 years is $ 680.24

3 0

3 years ago

Solve and graph the following inequality: 3(7x+17) > -19 + 14x

love history [14]

Answer:

Solving the inequality we get: $\mathbf{x>-7}$

Step-by-step explanation:

We need to solve and graph the inequality $3(7x+17) > -19 + 14x$

Solving:

$3(7x+17) > -19 + 14x$

Step 1: Multiply 3 with terms inside the bracket

$21x+51 > -19 + 14x$

Step 2:Subtracting 51 on both sides

$21x+51-51 > -19 + 14x-51\\21x>14x-70\\$

Step 3: Subtract 14x on both sides

$21x-14x>+14x-70-14x\\7x>-70$

Step 4: Divide both sides by 7

$\frac{7x}{7}>\frac{-70}{7}\\x>-10$

Solving the inequality we get: $\mathbf{x>-7}$

The graph is attached in the figure below.

5 0

3 years ago

Choose all the expressions that are equal to 7.6 ÷ 10. Please help me!

Mumz [18]

Answer:

a

Step-by-step explanation:

8 0

3 years ago

What is the area of a regular heptagon that has 4 inch sides and an apothem of 4.2 inches?

Lelu [443]

A = (1/2) * apothem * pperimeter
A = (1/2) * 4.2 * (4 * 7)
A = 58.8 inches

8 0

3 years ago