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levacccp [35]
2 years ago
11

For all values of x, f(x)=x-1 and g(x)=2x^2+3. Solve fg(x)=gf(x)

Mathematics
1 answer:
Phantasy [73]2 years ago
6 0

Answer:

x=3/4

Step-by-step explanation:

<u>Given:</u>

f(x) = x-1

g(x) = 2x²+3

<u>Evaluate composite functions:</u>

f(g(x)) = f(2x²+3) = (2x²+3)-1 = 2x²+2

g(f(x)) = g(x-1) = 2(x-1)²+3 = 2(x²-2x+1)+3 = 2x²-4x+2+3 = 2x²-4x+5

<u>Set expressions equal to each other and solve for x:</u>

2x²+2 = 2x²-4x+5

2 = -4x+5

-3 = -4x

3/4 = x

x = 3/4

Therefore, the value of x=3/4 satisfies both composite functions

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The figure below shows a quadrilateral ABCD with diagonal BD bisecting angle ADC:
juin [17]

Answer:

AD=DC

Step-by-step explanation:

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7 0
2 years ago
Find the HCF of 1045 and 1520 by long division. Method​ plsss
aliina [53]

Answer:

95

Step-by-step explanation:

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3 0
2 years ago
In a pen of goats and chickens, there are 40 heads and 150 feet. How many goats and chickens are in the pen?
s2008m [1.1K]

Hey there!!

A chicken has 1 head and 2 feet . A goat has 1 head and 4 feet

For heads, total = 40

Let us take the number of chickens as ' x ' and goats as ' y '

x + y = 40 ------------- ( 1 )

2x + 4y = 150 ----------- ( 2 )

Multiply the first equation with 2

2x + 2y = 80

2x + 4y = 150

Subtract the first equation from the first

2y = 70

y = 35

Number of goats = 35

substitute this in other equation

x + y = 40

x + 35 = 40

x = 5

Number of chickens are 4

Hope it helps!

6 0
3 years ago
A ballroom in a hotel has the shape shown. The manager needs to determine how much carpet is needed to recarpet this area. All a
Mars2501 [29]
Area of a rectangle=length x width


You have two rectangles:


First rectangle (the biggest):
length=9 yd
width=12 yd-6 yd=6 yd

Area of the biggest rectangle=(9 yd)(6 yd)=54 yd²

Second rectangle (the smallest)
length=6 yd
width=3 yd

Area of the smallest rectangle=(6 yd)(3 yd)=18 yd²

Area of the ballroom=area of the biggest rectangle + area of the smallest rectangle.

area of the ballroom=54 yd² +18 yd²=72 yd²
7 0
2 years ago
How can you decompose the composite figure to determine its area?
Anna007 [38]

For this case the first thing you should do is observe that the diameter of the four semicircles is the same.

Therefore, we can decompose the figure as follows:


1) We draw the diameters of the four semicircles to form a square.


2) We divide the figure into a square and four semicircles


3) The total area is the sum of the area of the square, plus the area of the 4 semicircles.


Answer:

c)as a square and four semicircles


5 0
3 years ago
Read 2 more answers
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