Find the value of h(45) for the function below.
h(x) = {(90 – 5)
what’s the value

Inverse Functions

One-to-one

Suppose f : A ⇥ B is a function. We call f one-to-one if every distinct

pair of objects in A is assigned to a distinct pair of objects in B. In other

words, each object of the target has at most one object from the domain

assigned to it.

There is a way of phrasing the previous definition in a more mathematical

language: f is one-to-one if whenever we have two objects a, c ⇤ A with

a ⌅= c, we are guaranteed that f(a) ⌅= f(c).

Example. f : R ⇥ R where f(x) = x2 is not one-to-one because 3 ⌅= 3

and yet f(3) = f(3) since f(3) and f(3) both equal 9.

Horizontal line test

If a horizontal line intersects the graph of f(x) in more than one point,

then f(x) is not one-to-one.

The reason f(x) would not be one-to-one is that the graph would contain

two points that have the same second coordinate – for example, (2, 3) and

(4, 3). That would mean that f(2) and f(4) both equal 3, and one-to-one

functions can’t assign two dierent objects in the domain to the same object

of the target.

If every horizontal line in R2 intersects the graph of a function at most

once, then the function is one-to-one.

Examples. Below is the graph of f : R ⇥ R where f(x) = x2. There is a

horizontal line that intersects this graph in more than one point, so f is not

one-to-one.

66

Inverse Functions

One-to-one

Suppose f : A —* B is a function. We call f one-to-one if every distinct

pair of objects in A is assigned to a distinct pair of objects in B. In other

words, each object of the target has at most one object from the domain

assigned to it.

There is a way of phrasing the previous definition in a more mathematical

language: f is one-to-one if whenever we have two objects a, c e A with

a ~ c, we are guaranteed that f(a) $ f(c).

Example. f : IR —* JR where f(x) = x2 is not one-to-one because 3 ~ —3

and yet f(3) = f(—3) since f(3) and f(—3) both equal 9.

Horizontal line test

If a horizontal line intersects the graph of f(.x) in more than one point,

then f(z) is not one-to-one.

The reason f(x) would not be one-to-one is that the graph would contain

two points that have the same second coordinate — for example, (2,3) and

(4,3). That would mean that f(2) and f(4) both equal 3, and one-to-one

functions can’t assign two different objects in the domain to the same object

of the target.

If every horizontal line in JR2 intersects the graph of a function at most

once, then the function is one-to-one.

Examples. Below is the graph of f : JR —, R where f(z) = z2. There is a

horizontal line that intersects this graph in more than one point, so f is not

Explanation:

Note: The equation I'm giving an answer to looks like this h(x)=1/9(90-x) the answer is 5

Explanation:

Because h(x) is the same as a Y in the formula y=mx+b so 5 = 1/9(90-x) which is the value of 45.

i discarded the supernatant and kept the pellet in this part of the experiment because you have to return all unused chemicals into their original containers at the end of each labratory.

explanation:

the soviet union wanted to impose communist governments in eastern europe.