T F (f o g)(X) = (g o f)(X)?

Question

True or False?

Answer 1

False in general. Putting on shoes and then putting on socks is different than putting on socks and then putting on shoes.

Answer 2

Technically, the answer is FALSE. In math, if a statement is not always true, then it must be considered false. This does not mean that the statement can never be true.

If f(x) and g(x) are inverse functions, then (f o g)(x) = (g o f)(x).

Most of the time, however, the composites are not equal.

Answer 3

None of the above. Sometimes true, sometimes false.

f(x) = x^2
g(x) = x^3 True

f(x) = x+5
g(x) = x+9 True

f(x) = x^2
g(x) = x+9 False

Answer 4

Give numerical values to test this equation.
f = 2
o= 3
g = 4
X =5
Left side of the equation: 120
Now, apply the same rule to the right side: 120

So, it is true.
This makes sense. Because they are multiplicants. It does not matter which order they are multiplied.

Answer 5

False; consider this example: g(x)=2x and f(x)=4+x. (f o g)(x)=4+2x and (g o f)(x)=8+2x. Clearly not equal.

Answer 6

False. In (f o g)(x), x is plugged into g first, and the resulting value is plugged into f. In (g o f)(x), x is plugged into f first, and the resulting value is plugged into g.

Answer 7

False

let f(x)=2x
and g(x)=x^2

then (fog)(x) = f(g(x)) = f(x^2) = 2x^2
(gof)(x) = g(f(x)) = g(2x) = (2x)^2 = 4x^2

Answer 8

I really like mathematician's answer. :)