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3 years ago

The composition of a fuction and its inverse is always

Mathematics

2 answers:

Dmitriy789 [7]3 years ago

5 0

Answer: x

In other words, the input variable

If f(x) is some function and g(x) is its inverse, then these two properties are always true for every x value in the domain of f(x) and g(x)

$f(g(x)) = x$

$g(f(x)) = x$

An example:

Let f(x) = x/3, then g(x) = 3x. The f(x) function takes the input and divides by 3, while the g(x) inverse function does the opposite and multiplies inputs by 3. The two opposite operations cancel out to leave the original input. If you were to say plug in x = 27, then f(27) = 9 which is then plugged into g(x) to get g(9) = 27. Therefore, g( f(27) ) = g( 9 ) = 27. The same idea works in reverse too.

levacccp [35]3 years ago

4 0

Answer:

oPPOSIT OF EACH OTHER.

Step-by-step explanation:

imagine 2x+4=6 and trying 2/4x+3=-1. those are the same or opposite

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Help please !!! (will give thanks )

Anestetic [448]

Answer:

The answer is -a-bc+43

Step-by-step explanation:

Pull terms out from under the radical, assuming positive real numbers

6 0

2 years ago

María is making fruto punch for her family reunión. She uses 6 quarts of ginger ale, 8 quarts of lemonade, and 10 quarts of rasp

expeople1 [14]

Answer:

6 gallons of punch makes her recipe.

Step-by-step explanation:

Given:

Quarts of ginger ale (g) = 6

Quarts of lemonade (l) = 8

Quarts of raspberry (r) = 10

Therefore, the total volume of fruto punch is equal to the sum of the volume of each of its ingredients.

So, Total volume = $g+l+r$

Total volume = 6 + 8 + 10 = 24 quarts

Now, we know that,

1 quart = 0.25 gallons

Therefore, from unitary method,

24 quarts = 24 × 0.25 = 6 gallons of punch

Therefore, 6 gallons of punch makes her recipe.

3 0

3 years ago

Read 2 more answers

Maria borrowed $120,000 from a bank when she bought her co-op for $156,000.

ANTONII [103]

Answer:

hello there im sam and im going to help you with your answer.

Step-by-step explanation:

so you take the 156,000 and subtract it to 120,000 and you will get 36,000 and thats how much she owes the bank.

6 0

2 years ago

A bakery sells hollow chocolate spheres. The larger diameter of each sphere is 4cm. The thickness of the chocolate of each spher

Nadusha1986 [10]

Answer:

3.5 cm

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

∆ABC has vertices A(–2, 0), B(0, 8), and C(4, 2)

Natali [406]

Answer:

Part 1) The equation of the perpendicular bisector side AB is $y=-\frac{1}{4}x+\frac{15}{4}$

Part 2) The equation of the perpendicular bisector side BC is $y=\frac{2}{3}x+\frac{11}{3}$

Part 3) The equation of the perpendicular bisector side AC is $y=-3x+4$

Part 4) The coordinates of the point P(0.091,3.727)

Step-by-step explanation:

Part 1) Find the equation of the perpendicular bisector side AB

we have

A(–2, 0), B(0, 8)

step 1

Find the slope AB

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{8-0}{0+2}$

$m=4$

step 2

Find the slope of the perpendicular line to side AB

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

therefore

The slope is equal to

$m=-\frac{1}{4}$

step 3

Find the midpoint AB

The formula to calculate the midpoint between two points is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

substitute the values

$M(\frac{-2+0}{2},\frac{0+8}{2})$

$M(-1,4)$

step 4

Find the equation of the perpendicular bisectors of AB

the slope is $m=-\frac{1}{4}$

passes through the point $(-1,4)$

The equation in slope intercept form is equal to

$y=mx+b$

substitute

$4=(-\frac{1}{4})(-1)+b$

solve for b

$b=4-\frac{1}{4}$

$b=\frac{15}{4}$

$y=-\frac{1}{4}x+\frac{15}{4}$

Part 2) Find the equation of the perpendicular bisector side BC

we have

B(0, 8) and C(4, 2)

step 1

Find the slope BC

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{2-8}{4-0}$

$m=-\frac{3}{2}$

step 2

Find the slope of the perpendicular line to side BC

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

therefore

The slope is equal to

$m=\frac{2}{3}$

step 3

Find the midpoint BC

The formula to calculate the midpoint between two points is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

substitute the values

$M(\frac{0+4}{2},\frac{8+2}{2})$

$M(2,5)$

step 4

Find the equation of the perpendicular bisectors of BC

the slope is $m=\frac{2}{3}$

passes through the point $(2,5)$

The equation in slope intercept form is equal to

$y=mx+b$

substitute

$5=(\frac{2}{3})(2)+b$

solve for b

$b=5-\frac{4}{3}$

$b=\frac{11}{3}$

$y=\frac{2}{3}x+\frac{11}{3}$

Part 3) Find the equation of the perpendicular bisector side AC

we have

A(–2, 0) and C(4, 2)

step 1

Find the slope AC

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{2-0}{4+2}$

$m=\frac{1}{3}$

step 2

Find the slope of the perpendicular line to side AC

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

therefore

The slope is equal to

$m=-3$

step 3

Find the midpoint AC

The formula to calculate the midpoint between two points is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

substitute the values

$M(\frac{-2+4}{2},\frac{0+2}{2})$

$M(1,1)$

step 4

Find the equation of the perpendicular bisectors of AC

the slope is $m=-3$

passes through the point $(1,1)$

The equation in slope intercept form is equal to

$y=mx+b$

substitute

$1=(-3)(1)+b$

solve for b

$b=1+3$

$b=4$

$y=-3x+4$

Part 4) Find the coordinates of the point of concurrency of the perpendicular bisectors (P)

we know that

The point of concurrency of the perpendicular bisectors is called the circumcenter.

Solve by graphing

using a graphing tool

the point of concurrency of the perpendicular bisectors is P(0.091,3.727)

see the attached figure

5 0

3 years ago