F (x)=|x-5|+|x+5|. Write f(x) as a piecewise function.?

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Answer 1 · 2018-04-18T12:30:07

Please see the explanation below

The function is

$f (x) = | x - 5 | + | x + 5 |$ $f(x)=|x-5|+|x+5|$

$x - 5 \geq 0$ $x-5>=0$ , $\Rightarrow$ $=>$ , $x \geq 5$ $x>=5$

$x + 5 \geq 0$ $x+5>=0$ , $\Rightarrow$ $=>$ , $x \geq - 5$ $x>=-5$

When $x < - 5$ $x<-5$

$f (x) = - x + 5 - x - 5 = - 2 x$ $f(x)=-x+5-x-5=-2x$

When $- 5 \leq x \leq 5$ $-5<=x<=5$

$f (x) = x + 5 - x + 5 = 10$ $f(x)=x+5-x+5=10$

When $x > 5$ $x>5$

$f (x) = x - 5 + x + 5 = 2 x$ $f(x)=x-5+x+5=2x$

$f(x)={(-2x, "if " x <-5), (10, "if " -5<=x>=5), (2x, "if " x >5):}$

graph{|x-5|+|x+5| [-22.08, 23.52, 2.17, 24.98]}