How do you write the piecewise function for |f(x)| and f(|x|) if, for example, its f(x)=X^2-9?

Question

527 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-14T12:25:05

See explanation.

In your example,

#f(x)=x^2-9 <=0#,, when #x^2-9<=0# i.e. when #x in [-3, 3].#.

So, the piecewise definition for #g(x)=|f(x)| # is

#g(x)=x^2-9, x in [-3, 3]# and

#=-f(x)=- (x^2-9) #, x outside #[-3, 3].#

Let h(x) = f(|x|= |x|^2-9=x^2-9=f(x).

So, for your example, there is no need for piecewise definition

To define #f(|x|), x <=0#, change x to -x, in every term of f(x).

For example, if #f(x)=x+x^2 and h(x)=f(|x|)#, then

#h(x) = x+x^2, x >=0# and

#=(-x)+(-x)^2=-x+x^2, x<=0#