Composition of Functions: Finding g(f-1(x)) with Given Equations

  • Thread starter Darknes51986
  • Start date
In summary, a Compositions math problem involves determining the number of ways in which a set of elements can be combined or arranged while meeting certain conditions. The key elements of a Compositions math problem include the total number of elements in the set, the size of the subsets being formed, and any given conditions. To solve a Compositions math problem, one must identify these key elements and use mathematical techniques such as combinations, permutations, or counting principles. Real-life applications of Compositions math problems include games of chance, combinations of a set of objects, and problems in probability and statistics. Some tips for solving Compositions math problems include carefully reading and understanding the given conditions, breaking the problem down into smaller parts, and using appropriate mathematical formulas or techniques
  • #1
Darknes51986
10
0

Homework Statement



Given: f(x)= 1/3x + 2 and g(x)= 2x2- x + 7

Find: g(f-1(x))

Homework Equations


The Attempt at a Solution



x=1/3y + 2
1/3y= x - 2
y=(x-2)/(1/3)
y=3x-6= f-1(x)

2(3x-6)2 + (3x-6) +7
solved to get..
18x2-69x+71
 
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  • #2


I got a different answer but your method is correct. You have a sign error somewhere.
 
  • #3


2(36)- 6+ 7= 72+1= 73, not 71.
 
  • #4


g(x)= 2x² - x + 7

2(3x-6)² + (3x-6) + 7
 

1. What is a Compositions math problem?

A Compositions math problem is a type of math problem that involves determining the number of ways in which a set of elements can be combined or arranged, while satisfying certain conditions or restrictions.

2. What are the key elements of a Compositions math problem?

The key elements of a Compositions math problem are the total number of elements in the set, the size of the subsets being formed, and any additional conditions or restrictions given in the problem.

3. How do you solve a Compositions math problem?

To solve a Compositions math problem, you must first identify the key elements and any given conditions. Then, you can use various mathematical techniques such as combinations, permutations, or counting principles to determine the total number of possible combinations or arrangements.

4. What are some real-life applications of Compositions math problems?

Compositions math problems have various real-life applications, including determining the number of possible outcomes in games of chance, calculating the number of ways to form different combinations of a set of objects, and solving problems in probability and statistics.

5. What are some tips for solving Compositions math problems?

Some tips for solving Compositions math problems include carefully reading and understanding the given conditions, breaking the problem down into smaller, more manageable parts, and using appropriate mathematical formulas or techniques to solve for the desired outcome.

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