If lim x->1 [f(x)-8]/[x-1] = 10, find lim x-> 1 f(x)

[grapz]

If lim x ---> 1 f( x ) - 8 / x - 1 = 10

find the lim x --> 1 f (x)

So i just rearrange for F(X) and i get f(x) = 10 x - 2

then i put 10(1) - 2 = 8

However i don't know if this method is acceptable. The answer is right but i am skeptical

 

[galactus]

You found f(x) OK.

You did good.

\(\displaystyle \L\\\lim_{x\to\1}(10x-2)=8\)

10x-2 is a line. It's continuous, therefore, you can sub x=1 right in.

Your method is acceptable.