Please explain how to do this please? The equation is f(x)=4x+10. Assign any number to x. Using complete sentences, explain whether f(g(x)) and g(f(x)) will result in the same number.

Question

Please explain how to do this please? The equation is f(x)=4x+10.  Assign any number to x. Using complete sentences, explain whether f(g(x)) and g(f(x)) will result in the same number.

savannah_noelle · Answer

@jim_thompson5910  @satellite73 Please help?

anonymous · Answer

what is $g(x)$?

anonymous · Answer

in general $f(g(x))$ is not equal to $g(f(x))$  
where you given a specific $g$ to use?

anonymous · Answer

help me out here...

savannah_noelle · Answer

This is what I was given. I'm on number 6.

anonymous · Answer

lol

anonymous · Answer

this must be the dumbest problem of the day
no matter, we can still solve if
you have 
$$f(x)=4x+10$$ now lets pick a $g$
i pick a simple one $g(x)=x^2+1$

anonymous · Answer

then we pick a number
i pick 2 so 
$$f(2)=4\times 2+10=14$$ and therefore 
$$g(f(2))=g(14)=14^2+1=197$$

anonymous · Answer

now 
$$g(2)=2^2+1=5$$ and so 
$$f(g(2))=f(5)=4\times 5+10=30$$

anonymous · Answer

and we see that 
$$f(g(2))=30, g(f(2))=197$$ and so
$$f(g(2))\neq g(f(2))$$

savannah_noelle · Answer

Thank you so much! This helped a lot. (:

anonymous · Answer

yw

savannah_noelle · Answer

@satellite73 for this step: hen we pick a number
i pick 2 so 
f(2)=4×2+10=14
how did you get 14?

ybarrap · Answer

It was just an error, you can correct. The point is that f(g) is not equal to g(f) generally. You will find this when you correct in his example. Question is pretty funny though.

anonymous · Answer

lol i made a mistake, that is how

savannah_noelle · Answer

Thanks @ybarrap @satellite73 (: lol yeah, the question is pretty lame. I ended up calling my teacher and his response was "God that question is so stupid, it could have definitely been re-worded."