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3 years ago

For the functions f(x)=4x−3 and g(x)=3x2+4x, find (f∘g)(x) and (g∘f)(x).

Mathematics

1 answer:

barxatty [35]3 years ago

7 0

Answer:

(16x + 21) and (16x - 6)

Step-by-step explanation:

f(g(x)) = f(6 + 4x)

Applying the f(x) function on (6 + 4x) gives

4(6 + 4x) - 3

Which equals 16x + 24 - 3

= 16x + 21

g(f(x)) = g(4x - 3)

Applying the g(x) function on (4x - 3) gives

6 + 4(4x - 3)

Which equals 6 + 16x - 12

= 16x - 6

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Find the distance between the points (-3,2) and (0,3).

Alex777 [14]

Answer:

The distance between (-3, 2) and (0,3) is √10.

Step-by-step explanation:

As we go from (-3,2) to (0,3), x increases by 3 and y increases by 1.

Think of a triangle with base 3 and height 1. Use the Pythagorean Theorem to find the length of the hypotenuse, which represents the distance between the points (-3, 2) and (0, 3):

distance = √(3² + 1²) = √10

The distance between (-3, 2) and (0,3) is √10.

7 0

3 years ago

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Could someone help me? Thanks <3

earnstyle [38]

Answer:

Step-by-step explanation:

100 - 35 = 55 dollars remaining

55/20 = 3.25 hours until no money

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3 years ago

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Find the degree of the term -5x to the power of 4

marysya [2.9K]

Answer:

4 or -625x^4 (Just in case I misunderstood)

Step-by-step explanation:

The degree is always the power of something. Since -5x has a power of 4, its degree is 4.

Just in case I misunderstood the question, I will solve it another way that I think you meant. (-5x)^4 is -5^4 times x^4.

-625 times x^4 is -625x^4.

5 0

3 years ago

In 1993, the sports league introduced a salary cap that limits the amount of money spent on players' salaries. The quadratic mod

jeyben [28]

Answer:

1999

Step-by-step explanation:

y = 0.2313(y - 1992)^2 + 2.600(y - 1992) + 35.17

verify with known data point

y = 0.2313(2004 - 1992)^2 + 2.600(2004 - 1992) + 35.17

y = 0.2313(12)^2 + 2.600(12) + 35.17

y = 27.9873 + 28.6 + 35.17

y = 99.6772 which verifies our equation

65 = 0.2313x² + 2.6x + 35.17

0 = 0.2313x² + 2.6x - 29.83

quadratic formula

x = (-2.6 ±√(2.6² - 4(0.2313)(-29.83))) / (2(0.2313))

x = (-2.6 + 5.86) / 0.4626 = 7.05 years

7.05 = y - 1992

y = 1999.05

8 0

3 years ago

I’m need this worked out step by step by tonight

Pie

9514 1404 393

Answer:

-3 ≤ x ≤ 19/3

Step-by-step explanation:

This inequality can be resolved to a compound inequality:

-7 ≤ (3x -5)/2 ≤ 7

Multiply all parts by 2.

-14 ≤ 3x -5 ≤ 14

Add 5 to all parts.

-9 ≤ 3x ≤ 19

Divide all parts by 3.

-3 ≤ x ≤ 19/3

_____

<em>Additional comment</em>

If you subtract 7 from both sides of the given inequality, it becomes ...

|(3x -5)/2| -7 ≤ 0

Then you're looking for the values of x that bound the region where the graph is below the x-axis. Those are shown in the attachment. For graphing purposes, I find this comparison to zero works well.

For an algebraic solution, I like the compound inequality method shown above. That only works well when the inequality is of the form ...

|f(x)| < (some number) . . . . or ≤

If the inequality symbol points away from the absolute value expression, or if the (some number) expression involves the variable, then it is probably better to write the inequality in two parts with appropriate domain specifications:

|f(x)| > g(x) ⇒ f(x) > g(x) for f(x) > 0; or -f(x) > g(x) for f(x) < 0

Any solutions to these inequalities must respect their domains.

8 0

3 years ago