# math

The function
f(x) = cx/2x+3
satisfies f(f(x))=x for all real numbers x\= -3/2. Find c.

1. f(x) = cx/(2x+3)
f(f) = cf/(2f+3) = c[cx/(2x+3)]/(2[cx/(2x+3)]+3)
= c^2x/(2(c+3)x+9)

So, if
c^2x/(2(c+3)x+9) = x,
c^2x = 2(c+3)x^2 + 9x
2(c+3)x^2 + (9-c^2)x = 0
x(2c+6+9-c^2) = 0
x(15+2c-c^2) = 0
x(5c-1)(3c+1) = 0
So, c = 1/5 or c = -1/3

posted by Steve

## Similar Questions

1. ### Math

The twice–differentiable function f is defined for all real numbers and satisfies the following conditions: f(0)=3 f′(0)=5 f″(0)=7 a)The function g is given by g(x)=e^ax+f(x) for all real numbers, where a is a
2. ### math

The function f(x) = cx/2 x+3 satisfies f(f(x))=x for all real numbers x\= -3/2. Find c.
3. ### ALgebra

The function f(x) = cx/2x+3 satisfies f(f(x))=x for all real numbers x\= -3/2. Find c. (\= does not equal)
4. ### Maths

Given that a and b are real numbers and that x satisfies the inequality ax>=b when x>=14, what is the smallest integer x that satisfies ax>a+2b ?
5. ### maths

Given that a and b are real numbers and that x satisfies the inequality ax>=b when x>=75, what is the smallest integer x that satisfies ax>a+2b ?
6. ### Math- calculus

Suppose f is a function which satisfies the properties: f(x+y)=f(x)+f(y)+x2y+xy2 for all real numbers x and y, and limx→0f(x)x=1. f′(x) thanks in advance!
7. ### Algebra

The function f:R⇒R satisfies xf(x)+f(1-x)=x^3-x for all real x. Find f(x).
8. ### Pre-Calculus

A rectangle is bounded by the x-axis and the semicircle y = √36 – x2, as shown in the figure below. Write the area A of the rectangle as a function of x, and determine the domain of the area function. A = all real numbers
9. ### Algebra :P... again

Hi! Sorry.. but 1 more question? Direction: Find the domain of the function. Problem: y = - 1 0 / 1 1 - x [A] All real numbers except x= -11 [B] All real numbers except x= 0 [C] All real numbers except x= 10 [D] All real numbers
10. ### Math

What is the domain and range fro the expentiral function f(x)=-2x4^x-1+3? Domain:all real numbers Range:all real numbers less than 3 Domain:all real numbers Range:all real numbers greater than 3 Domain: all real numbers greater

More Similar Questions