Respuesta :
Given:
Consider the piecewise function is
[tex]f(x)=\left \{\begin{matrix}x^2+4x,\text{ if } x\leq -1\\ x, \text{ if }-1<x\leq 1\\-1,\text{ if }x>1\end{Matrix}\right.[/tex]
To find:
The value of the function at indicated values.
Solution:
We know that, [tex]-2,-\dfrac{3}{2},-1[/tex] are less than or equal to -1. So, for these values the function is [tex]f(x)=x^2+4x[/tex].
For x=-2,
[tex]f(-2)=(-2)^2+4(-2)[/tex]
[tex]f(-2)=4-8[/tex]
[tex]f(-2)=-4[/tex]
Similarly,
For [tex]x=-\dfrac{3}{2}[/tex].
[tex]f(-\dfrac{3}{2})=(-\dfrac{3}{2})^2+4(-\dfrac{3}{2})=-\dfrac{15}{4}[/tex]
For [tex]x=-1[/tex].
[tex]f(-1)=(-1)^2+4(-1)=-3[/tex]
We know that, 0 is lies between -1 and 1. So, for this values the function is [tex]f(x)=x[/tex].
For x=0,
[tex]f(0)=0[/tex]
We know that, 25 is greater than 1. So, for this values the function is [tex]f(x)=-1[/tex].
For x=25,
[tex]f(25)=-1[/tex]
Therefore, the required values are, [tex]f(-2)=-4, f(-\dfrac{3}{2})=-\dfrac{15}{4},f(-1)=-3,f(0)=0,f(25)=-1[/tex].
