Evaluate, if possible, f(x)=x^3-x ;

f(x)-f(1) / x-1

Question

Evaluate, if possible, f(x)=x^3-x   ;

f(x)-f(1) / x-1

anonymous · Answer

@ash2326

ash2326 · Answer

We have 
$$f(x)=x^3-x$$
Let's find f(1), can you find that? @schmidtdancer

anonymous · Answer

Ok yes, it would be f(1)=1-1 which is 0?

ash2326 · Answer

okay, let's work to find that
$$\frac{f(x)-f(1)}{x-1}$$
f(1)=0  and f(x)=x^3-x
$$\frac{f(x)-f(1)}{x-1}=\frac{x^3-x-0}{x-1}=\frac{x^3-x}{x-1}$$
Can you simplify this?

anonymous · Answer

x^3-x/x-1?

ash2326 · Answer

yeah, factor the numerator, will you?

anonymous · Answer

x(x^2-1)/x-1

ash2326 · Answer

we could simplify it more
$$\frac{x(x+1)(x-1)}{x-1}$$
now we can cancel the (x-1) from numerator and denominator provided $x\ne 1$
if x=1 the expression becomes $\huge\frac 00$, it's an indeterminate form.
so assuming \(x\ne 1), cancel the (x-1) s @schmidtdancer

anonymous · Answer

Yeah, ok so it is x(x+1) now

ash2326 · Answer

yeah. that's our final expression under the condition that $x\ne1$

anonymous · Answer

Ok so I would put x(x+1) as my answer and include x doesn't equal 1?

ash2326 · Answer

yeah