Simplifying functions

[Smellyface]

Hey there, I have a functions problem I can't seem to get right.

For the function f(x)=x^2+9x simplify the following expression as much as possible:

[f(w)-f(x)]/(w-x) w?x

This is how I went about it:

[f(w-x)]/(w-x)

[(w-x)^2+9(w-x)]/(w-x)

w-x+9

However it says the answer isn't right. I got the right answer of a similar question by using the same method but I can't get this one, any help would be greatly appreciated! Thanks in advance.

 

[Deleted member 4993]

Hey there, I have a functions problem I can't seem to get right.

For the function f(x)=x^2+9x simplify the following expression as much as possible:

[f(w)-f(x)]/(w-x) w?x

This is how I went about it:

[ f(w-x) ]/(w-x) <<< Where did that come from?

[(w-x)^2+9(w-x)]/(w-x)

w-x+9

However it says the answer isn't right. I got the right answer of a similar question by using the same method but I can't get this one, any help would be greatly appreciated! Thanks in advance.

 

[Smellyface]

Working with functions, these things are equal to each other:

x(f+g) = f(x)+g(x)
x(f-g) = f(x)-g(x)
x(f*g) = f(x)*g(x)
x(f/g) = f(x)/g(x)
(fog) = f(g(x))

Correct?
which is why f(w)-f(x) = f(w-x).

This is the first question i worked on:
f(x)=x^2+9x

[f(x+h)-f(x)]/h h?0
([(x+h)^2+9(x+h)]-(x^2+9x))/h
(2hx+h^2+9h)/h
2x+h+9 Answer is correct

So as you can see i did pretty much the same thing but first changed f(w)-f(x) to f(w-x) so i could put in the number. Maybe that's where I'm going wrong

 

[Deleted member 4993]

Working with functions, these things are equal to each other:

x(f+g) = f(x)+g(x)
x(f-g) = f(x)-g(x)
x(f*g) = f(x)*g(x)
x(f/g) = f(x)/g(x)
(fog) = f(g(x))

No - in general these are not correct. Please read up on Linear function, Inverse function and principle of superposition.

Correct?
which is why f(w)-f(x) = f(w-x).

This is the first question i worked on:
f(x)=x^2+9x

[f(x+h)-f(x)]/h h?0
([(x+h)^2+9(x+h)]-(x^2+9x))/h
(2hx+h^2+9h)/h
2x+h+9 Answer is correct

So as you can see i did pretty much the same thing but first changed f(w)-f(x) to f(w-x) so i could put in the number. Maybe that's where I'm going wrong

f(x) = x[sup:3vrv50x5]2[/sup:3vrv50x5] - 9x ................ not a linear function

f(w) = w[sup:3vrv50x5]2[/sup:3vrv50x5] - 9w

f(w) - f(x) = -x[sup:3vrv50x5]2[/sup:3vrv50x5] + 9x + w[sup:3vrv50x5]2[/sup:3vrv50x5] - 9w = (w - x) * (w + x - 9)

Now continue.....