Posted by ayotal on Wednesday, October 19, 2011 at 6:20pm.
In mathematics, you cannot prove that a statement is true by a finite number of examples, because it is not possible to prove all possible cases by a finite number of examples.
However, to prove that a statement is false, you only need ONE counter-example. This is probably your case here.
Try
f(x)=x^2+2,
g(x)=x+2
then fog(x)=f(g(x))=(x+2)^2+2
gof(x)=x^2+4
Since we demonstrated fog(x)≠gof(x), the given statement is not true.
On the other hand, if we define
f(x)=2x, g(x)=4x
then fog(x)=f(4x)=8x^2
gof(x)=g(2x)=8x^2
so fog(x)=gof(x) in this case, BUT it does not prove anything.
Related Questions
Algebra - Use composition of functions to show that the functions f(x) = 5x + 7 ...
Composite Functions - f(x)=(7x+28)/(x-3) and g(x)=(3x+28)/(x-7) Find: (fog)(x) (...
Composite Functions - Find the composite functions for the given functions. (6 ...
Calculus - Hi there, I need help with composition of functions. I need to find ...
math - how to you find a composite function form of y in this problem? y = 1/[(x...
math - Solve the two sided inequality and show the solution on real line 7 &...
calculus - Given two functions as: f(x) = x2-x-1 and g(x) = 3/x Find fog(x) ...
Calculus - We're learning about different kinds of functions and I don't...
math - Solve the two sided inequality and show the solution on real line 7 &...
CALCULUS - show that f(x) = x^2-1 (x is greater than and equal to 0) and g(x) = ...
For Further Reading
