How to solve -8x+2-16<5x+7x

Answer:

is

Step-by-step explanation:

Property of inverse function:

The function should be bijective function ( one-to-one and onto)

Option A) f(x)=|x-4|+1

It is absolute function. Not one-to-one function.

Domain: All real (-∞,∞)

Range: [1,∞)

False ( Inverse not possible )

Option B)

It is quadratic function. Not one-to-one function.

Domain: All real (-∞,∞)

Range: [0,∞)

False ( Inverse not possible )

Option C)

It is polynomial function with even degree. Not one-to-one function.

Domain: All real (-∞,∞)

Range: [0,∞)

False ( Inverse not possible )

Option D)

It is linear function. one-to-one and onto

Domain: All real (-∞,∞)

Range: All real (-∞,∞)

True ( Inverse possible )

Inverse of is

Hence, The function inverse function is

Answer: Hello there!

A function only can have an inverse if the function is injective and surjective (and continuous):

Then we need to see; if f(x1) = f(x2) = y, and x1 is different from x2, then f(x) has not an inverse:

a) f(x) = Ix - 4I + 1

for example, f(0) = I-4I + 1 = 5

and f(8) = I8 -4I + 1 = 4 + 1 = 5

then f(x) does not have an inverse

b) f(x) = 25x^2 + 70x + 49

This is a cuadratic function, wich is graphed as a arc going up or down, wich means that there are two values of x that give the same value for f(x), then this function has not inverse. (this will be the case for all even powers)

c) f(x) = x^4

Again, an even power. But let's probe it:

f(1) = 1^4 = 1

f(-1) = (-1)^4 = 1

f(x) does not have an inverse:

d) f(x) = x + 3/7

Ok, here we have a linear equation, wich means that is injective and surjective.

The inverse of this function can be g(x) = x - 3/7

proof:

f(g(x)) = f( x - 3/7) = (x - 3/7) + 3/7 = x

then f and g are inverses of each other.

(if in this case f(x) = (x + 3)/7 = x/7 + 3/7 is also a linear equation, so it is injective and surjective (and continuous), wich implies that has an inverse)

Answer: ~ 34.15%

Step-by-step explanation:

To calculate the percent error for the amount of snowfall, you can use the following formula:

Percent Error = [(|Estimated Value - Actual Value|) / Actual Value] * 100%

In this case, the estimated snowfall is 6.75 inches, and the actual snowfall is 10.25 inches. Plugging these values into the formula:

Percent Error = [(|6.75 - 10.25|) / 10.25] * 100%

Percent Error = [(3.5) / 10.25] * 100%

Percent Error ≈ 34.15%

So, the percent error for the amount of snowfall is approximately 34.15%. This means that the estimated snowfall was about 34.15% lower than the actual snowfall.

Answer:

The total number of handshakes that would happen between the three people are:

                                    3

Step-by-step explanation:

There are three people at a party.

Let they be denoted by A,B and C.

Now, the total number of handshakes that would occur will be denoted by:

      AB, AC and BC

where AB denotes that A and B shake hands.

AC denote that A and C shake hands.

and BC denote that B and C shake hands.

Hence, total number of handshakes are:

                           3

2.1 is rounded to the nearest tenth

.1 is a tenth

.01 is hundredth

Answer:

150 vouchers to wash trucks were sold

250 vouchers to wash compact cars were sold

Step-by-step explanation:

Here, we are interested in calculating the number of each type of vouchers sold.

Let the number of vouchers to wash trucks be x while the number of vouchers to wash compact trucks be y.

Firstly, we know that both sums up to be 400.

Mathematically;

x + y = 400 •••••••••(i)

Secondly,

since a voucher to wash trucks sell $4, and we sold a total of x, the amount generated from selling is 4 * x = $4x

Same way for the vouchers to wash compact cars, we have a total of $3 * y = $3y

The sum of both gives $1350, which is the total sales.

Mathematically;

4x + 3y = 1350 ••••••(ii)

So we have two equations to solve simultaneously;

x + y = 400

4x + 3y = 1350

Multiply equation i by 4 , we have;

4x + 4y = 1600

4x + 3y = 1350

Subtract equation ii from i, we have 4y-3y = 1600-1350

y = 250

From equation 1, we know that

x + y = 400

This means that;

x = 400 -y

x = 400 -250

x = 150