for 7.52 you purchased 8 pens and highlighters from a local bookstore. Each highlighter cost $1.09 and each pen cost $.69. how many pens did you buy?

Answer:

We know that range is the set of outputs that shown on the y-axis of the graph, so we must find the endpoints of the graph on the y-axis. When we look, we get the endpoints -6 and 10, so we know that this is the range, and so we represent this in an expression:

-6 < y < 10

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)

Answer:

(- 1, 4 )

Step-by-step explanation:

x = 1 is a vertical line passing through all points with an x- coordinate of 1

The point P(3, 4) is to units to the right of x = 1.

Hence the refection will be 2 units to the left of x = 1

P' = (1 - 2, 4 ) = (- 1, 4 )

Answer:

Step-by-step explanation:

In triangle if two sides are known and included angle is known we can use cosine formula as follows:

Say in a triangle, sides a,b are known and also included angle C

Then the third side

Since all values on right side are known, we can find the third side c easily.

Case II:

If alternately two sides and one angle not included is known. i.e we know a,b and either angle A or B.

then to find third side we use sine formula.

Using the above we can find the unknonwn side c easily.