Question

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

Answer 1

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.

Answer 2

Check below for detailed solution

Explanation:

• `f` even means: for each `x` `in` `RR` , `-x` `in` `RR`

`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)`