Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

For example if $f(x) = x + 2$ and $g(x) = 4x - 1$

Then what would be the difference in $f \cdot g$ and $f(g(x))$?

share|cite|improve this question
2  
If the dot is meant to be the composite function then they are the same thing – John Jan 2 '14 at 16:40

The notation $f \cdot g$ means that for every $x$ the function is $$ (f \cdot g)(x) = f(x) \cdot g(x) $$ which is pointwise multiplication.

On the other hand $f \circ g$ is the composition of functions, $$ (f \circ g)(x) = f(g(x)) \ . $$

For your examples: $$ f(x) \cdot g(x) = (x+2) \cdot (4x-1) = 4x^2 + 8x - x - 2 = 4x^2 + 7x -2 $$ while $$ (f \circ g)(x) = f(g(x)) = f(4x-1) = (4x-1)+2 = 4x + 1 \ . $$

share|cite|improve this answer

If dot means composition then they are the same. $$(f \cdot g)(x) = f(g(x))=(4x-1)+2=4x+1$$ If dot means multiplication then $$(f \cdot g)(x)=(x+2)(4x-1)=4x^2+7x-2$$

share|cite|improve this answer

If your interpretation of $\cdot$ is $\circ$ as in $f \circ g(x)$ Then, $f \circ g(x)=f(g(x))$ which is a composite function. Note that $(f \circ g)(x) \neq (g \circ f)(x)$

share|cite|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.