$MathMaster logo$

MathMaster

Home
general
let the functions be f a b and g b c the composition of these two functions that is the composite of g with f is a functio

Question

Let the functions be f: A → B and g: B → C, the composition of these two functions, that is, the composite of g with f is a function h: A → C, such that h(x) = g(f(x )). let the functions be f(x)=x²-1 and g(x)=2x+2 what is the value of the composites

155

likes

773 views

Answer to a math question Let the functions be f: A → B and g: B → C, the composition of these two functions, that is, the composite of g with f is a function h: A → C, such that h(x) = g(f(x )). let the functions be f(x)=x²-1 and g(x)=2x+2 what is the value of the composites

$Expert avatar$

4.4

85 Answers

1. Determine

f(x)

:

f(x) = x^2 - 1

2. Substitute

f(x)

into

g(x)

:

g(f(x)) = g(x^2 - 1) = 2(x^2 - 1) + 2

3. Simplify the expression:

2(x^2 - 1) + 2 = 2x^2 - 2 + 2 = 2x^2

Therefore,

h(x) = 2x^2

Frequently asked questions (FAQs)

What is the surface area of a cylinder with a radius of 4 units and height of 10 units?

+

What are the roots of the cubic equation x^3 - 5x^2 + 4x + 12 = 0?

+

What is the integral of ∫(2x^3 + 5x^2 - 3x + 1) dx using the standard formulas?

+

New questions in Mathematics

a to the power of 2 minus 16 over a plus 4, what is the result?

Let f(x)=||x|−6|+|15−|x|| . Then f(6)+f(15) is equal to:

A book is between 400 and 450 pages. If we count them 2 at a time there is none left over, if we count them 5 at a time there is none left over and if we count them 7 at a time there are none left over, how many pages does the book have?

*Question!!* *Victory saved 3,000 in first bank and 2,000 Naira in union bank PSC with interest rate of X% and Y% per annual respectively his total interest in one year is #640. If she has saved 2,000 naira with first bank and 3,000 naira in union bank for same period she would have made extra 20# as additional interest, then find the value of X and Y

Additionally, the boss asked Armando to determine how many toy sales branches he would have in the fifteenth year, knowing that the first year they started with two branches, by the second they already had 5 branches and, by the third year, they had 8 branches. From the above, determine the number of branches it will have for the fifteenth year.

(6.2x10^3)(3x10^-6)

The director of a company must transfer 6 people from the human resources department to the sales department, in order to sustain sales during the month of December. What is the probability that he will transfer only 2 of them?

Answer the following questions regarding the expression below. 0.1 (a) Write the number as a fraction.

Nice's central library building is considered one of the most original in the world, as it is a mix between a sculpture and a work of habitable architecture. It was called La Tête Carrée and is made up of part of a bust that supports a cube divided into five floors. It is known that the building has a total height of approximately 30 meters. It admits that the cubic part of the sculpture is parallel to the floor and has a volume of 2744 meters3 Calculate, in meters, the height of the bust that supports the cube. Displays all the calculations you made.

Show this compound proposition to be true or false. Paris is the capital of England or Rome is the capital of Italy

A cell phone company offers two calling plans. Plan A: $20 per month plus 5 cents for each minute, or Plan B: $30 per month plus 3 cents for each minute. [2] Write an equation to describe the monthly cost (a) C (in $) in terms of the time m (in minutes) of phone calls when Plan A is applied.

A,B,C and D are the corners of a rectangular building. Find the lengths the diagonals if AB measures 38' - 9" and AD measures 56' - 3"

Which statement best describes the key changes in perspectives on inclusion? An inclusive program must consider the unique experiences of every child and family as well as the child's strengths and needs. There is a shift in thinking about individual programs as "inclusive programs" to thinking about inclusion as something that reflects the cultural influence of the family. There is a greater emphasis on barriers to full participation and the acknowledgement that all children are unique and must be fully and meaningfully engaged in a program. In an inclusive program all participants are accepted by their peers and other members of the community.

On Tuesday Shanice bought five hats.On Wednesday half of all the hats that she had were destroyed.On Thursday there were only 17 left.How many Did she have on Monday.

a) 6x − 5 > x + 20

2 - 6x = -16x + 28

A 20-year old hopes to retire by age 65. To help with future expenses, they invest $6 500 today at an interest rate of 6.4% compounded annually. At age 65, what is the difference between the exact accumulated value and the approximate accumulated value (using the Rule of 72)?

Dano forgot his computer password. The password was four characters long. Dano remembered only three characters: 3, g, N. The last character was one of the numbers 3, 5, 7, 9. How many possible expansions are there for Dano's password?

Exercise The temperature T in degrees Celsius of a chemical reaction is given as a function of time t, expressed in minutes, by the function defined on ¿ by: T (t )=(20 t +10)e−0.5t. 1) What is the initial temperature? 2) Show that T' (t )=(−10 t +15)e−0 .5t. 3) Study the sign of T' (t ), then draw up the table of variations of T . We do not ask for the limit of T in +∞. 4) What is the maximum temperature reached by the reaction chemical. We will give an approximate value to within 10−2. 5) After how long does the temperature T go back down to its initial value? We will give an approximate value of this time in minutes and seconds. DM 2: study of a function Exercise The temperature T in degrees Celsius of a chemical reaction is given as a function of time t, expressed in minutes, by the function defined on ¿ by: T (t )=(20 t +10)e−0.5t. 1) What is the initial temperature? 2) Show that T' (t )=(−10 t +15)e−0.5 t. 3) Study the sign of T' (t ), then draw up the table of variations of T . We do not ask for the limit of T in +∞. 4) What is the maximum temperature reached by the reaction chemical. We will give an approximate value to within 10−2. 5) After how long does the temperature T go back down to its initial value? We will give an approximate value of this time in minutes and seconds.