Suppose f(x) is even function. if f(x) is continous at a, show f(x) continuous at -a ?

2 Answers
Feb 24, 2018

See below

Explanation:

I'm not 100% sure about this, but this would be my answer.

The definition of an even function is f(-x)=f(x)

Therefore, f(-a)=f(a). Since f(a) is continuous and f(-a)=f(a), then f(-a) is also continuous.

Mar 9, 2018

Check below for detailed solution

Explanation:

  • f even means: for each xinRR , -xinRR

f(-x)=f(x)

  • f continuous at x_0=a <=> lim_(x->a)f(x)=f(a)

lim_(x->-a)f(x)

Set y=-x
x->-a
y->a

= lim_(y->a)f(-y)=lim_(y->a)f(y)=lim_(x->a)f(x)=f(a)