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4 years ago

For the functions f(x)=2x−5 and g(x)=3x2−x, find (f∘g)(x) and (g∘f)(x).

Mathematics

1 answer:

Law Incorporation [45]4 years ago

8 0

Hi,

f°g means : apply first g then f . so calculate "g" and then use result as "x" in f.

g°f means : you apply first f then g

so : f°g = 2(3x²-x) -5 = 6x²-2x- 5

To improve in math, you need practice. have a try with g°f :)

give the answer in comments, and I will tell you if you are correct.

good luck.

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The table shows sets of ordered pairs that form a relation.

tiny-mole [99]

A relation is a relationship between sets of values. In math, the relation is between the x-values and y-values of ordered pairs. The set of all x-values is called the domain of the relation, and the set of all y-values is called the range of the relation.

A relation from a set X (domain) to a set Y (range) is called a function if each element of X is related to exactly one element in Y.

A. A relation {(2,-3), (3,-3), (1,4), (9,2)} is a function, because each x has exactly one element y related to.

B. A relation {(8,-3), (3,8), (9,4), (-2,2)} is a function, because each x has exactly one element y related to.

C. A relation {(1,-1), (4,8), (9,-1), (3,2)} is a function, because each x has exactly one element y related to.

D. A relation {(1,-1), (-1,5), (1,-6), (-3,2)} is not a function, because x=1 has two possible outcomes y: y=-1 or y=-6.

Answer: A, B and C are functions and D is not a function

4 0

3 years ago

−5+6×52+56÷(−8) pllllll

grandymaker [24]

Answer:

Its 300.

hope this helps:)

7 0

3 years ago

Read 2 more answers

A student starts at (0,0) and walks to (12, 0), turns and then walks to (7,12). What is the total distance that this student wal

Harman [31]

Answer:

Step-by-step explanation:

(0,0) to (12,0) => the distance = 12

(12,0) to(7,12) => the distance =

√[(12-0)²+(7-12)²]=√(144+5) =√169 = 13

so, the total distance = 12+13 = 25

4 0

3 years ago

Factor f(x)=x4-x3-7x2+13x-6 completely. Then Sketch the graph

Dennis_Churaev [7]

ANSWER TO QUESTION 1

$f(x)=(x-2)(x+3)(x-1)^2$ .

EXPLANATION

The function given to us is,

$f(x)=x^4-x^3-7x^2+13x-6$

According to rational roots theorem,

$\pm1,\pm2,\pm3,\pm6$ are possible rational zeros of

$f(x)=x^4-x^3-7x^2+13x-6$ .

We find out that,

$f(-3)=(-3)^4-(-3)^3-7(-3)^2+13(-3)-6$

$f(-3)=81+27-63-39-6$

$f(-3)=6-6$

$f(-3)=0$

Also

$f(2)=(2)^4-(2)^3-7(2)^2+13(2)-6$

$f(2)=16-8-28+26-6$

$f(2)=6-6$

$f(2)=0$

This implies that

$x-2 and x+3$ are factors of

$f(x)=x^4-x^3-7x^2+13x-6$ and hence $(x-2)(x+3)=x^2+x-6$ is also a factor.

We perform the long division as shown in the diagram.

Hence,

$f(x)=(x-2)(x+3)(x-1)^2$ .

ANSWER TO QUESTION 2

Sketching the graph

We can see from the factorization that the roots

$x=2$ and $x=-3$ have a multiplicity of 1, which is odd. This means that the graph crosses the x-axis at this intercepts.

Also the root $x=1$ has a multiplicity of 2, which is even. This means the graph does not cross the x-axis at this intercept.

Now we determine the position of the graph on the following intervals,

$x\le -3$

$f(-4)=(-4)^4-(-4)^3-7(-4)^2+13(-4)-6$

$f(-4)=150\:>0$

$-3\le x \le 1$

$f(0)=-6\:$

$1\le x\le 2$

$f(1.5)=-0.56\:$

$x \ge 2$

$f(3)=24\:>0$

We can now use these information to sketch the function as shown in diagram

4 0

3 years ago

Mrs.Vaz said that 20% of the Legacy College Scholars will be attending the trip. There are 60 scholars attending the trip. How m

Musya8 [376]

Answer:

There are 300 scholars in total.

Step-by-step explanation:

300×0.20=60

5 0

4 years ago