MHB Given f(xy) = f(x)/y and f(500) = 3, find f(600)

  • Thread starter Thread starter mathtopamela
  • Start date Start date
Click For Summary
SUMMARY

The function f satisfies the equation f(xy) = f(x)/y for all positive real numbers x and y. Given that f(500) = 3, we can determine f(600) by substituting x = 500 and y = 6/5, resulting in f(600) = f(500(6/5)) = f(500) / (6/5). Therefore, f(600) equals 3 * (5/6), which simplifies to 2.5.

PREREQUISITES
  • Understanding of functional equations
  • Knowledge of algebraic manipulation
  • Familiarity with positive real numbers
  • Basic problem-solving skills in mathematics
NEXT STEPS
  • Study functional equations in depth
  • Explore properties of functions defined by multiplicative relationships
  • Learn about transformations of functions
  • Practice solving similar problems involving functional equations
USEFUL FOR

Mathematicians, students studying advanced algebra, educators teaching functional equations, and anyone interested in problem-solving techniques in mathematics.

mathtopamela
Messages
1
Reaction score
0
Help me understand the following problem:

Let f be a function satisfying f(xy) = f(x)/y for all positive real numbers x and y, and f(500) = 3.
What is f(600)?
 
Mathematics news on Phys.org
mathtopamela said:
Help me understand the following problem:

Let f be a function satisfying f(xy) = f(x)/y for all positive real numbers x and y, and f(500) = 3.
What is f(600)?

you are given f(500) = 3 or

x = 500, f(x) = 3

you need to calculate f(600) or xy = 600.

you can now calculate the value of y and then f(xy) or f(600)
 
600= 500(6/5) so f(600)= f(500(6/5)). (x= 500, y= 6/5)
 

Similar threads

MHB Solving for $f(600)$ Given $f(500)=3$
  • · Replies 3 ·
Replies
3
Views
2K
MHB Is $f(x) = xf(1)$ the only solution to the given functional equation?
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Finding the Largest (or smallest) Value of a Function - given some constant symmetric errors
  • · Replies 3 ·
Replies
3
Views
2K
MHB Determine all real valued differentiable functions f(x)+f(y)=f(xy)
  • · Replies 4 ·
Replies
4
Views
2K
MHB Finding $a$ and $b$ for $f(x)=|\lg (x+1)|$
  • · Replies 3 ·
Replies
3
Views
990
MHB Find Inverse of Rational Function
  • · Replies 7 ·
Replies
7
Views
2K
MHB Solving $x^3+y^3=7$ and $x^2+y^2+x+y+xy=4$ System of Equations
  • · Replies 1 ·
Replies
1
Views
1K
MHB Finding the Inverse of f(x) = x/(x+4)
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad The behavior of a potential-like integral at infinity
  • · Replies 21 ·
Replies
21
Views
2K
Undergrad Transformation of Functions: How Do Domain and Range Change?
  • · Replies 4 ·
Replies
4
Views
2K