the coordinates of a point on a coordinate grid are (−1, 5). the point is reflected across the x-axis to obtain a new point. the coordinates of the reflected point are (1, −5) (−1, 5) (1, 5) (−1, −5)

Answer:

Let x represent the weight of one steel ball. One side will have 8 balls or 8x and the other side will have 14-8 or 6 balls (6x) and the 20 gram weight. 8x = 6x + 20.

Answer:

The cost of one night at the hotel is $125

Step-by-step explanation:

Let the cost of each night spend in hotel is = $x

Let the cost of each day of car rented = $y

Cannor spent 3 nights at a hotel and rented a car for 4 days paid $675.

 ......(1)

Jillian also spent 4 nights in same hotel and rented a car for 5 days paid $875.

 .......(2)

Now, we solve equation (1) and (2) by substitution method

From (1) take the value of x,  

then put in equation (2)

solve,

 (Taking LCM)

Now, put value of in value of  

Therefore, the cost of one night at the hotel is $125

Answer:

C)

E)

F)

Step-by-step explanation:

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)