help with math1141 questions (1 Viewer)

[maths > english]

Suppose that <i>f</i> is a continuous at 0 and that for all x, y є R,<i> f </i>(<i>x</i> + <i>y</i>) = <i>f </i>(<i>x</i>) + <i>f </i>(<i>y</i>)

(a) Show that <i>f</i> (0) = 0.
(b) Prove that <i>f</i> is continuous at every point a є R.

im ok with part (a) but i have no idea how to do part (b).

 

[maths > english]

just thought of a way to do it (attached) but its very messy and theres definately got to be an easier way

can anyone think of a way that does not involve showing <i>f</i> (<i>a</i>) = -<i>f</i> (-<i>a</i>)?

 

[gman03]

Your way works anyway... Here is what my tutor gave me:

 

[maths > english]

thanks for your help