given the piecewise function shown below select all the statements that are true

The piecewise function tells us specific rules he should execute based on the input x we put in. For example for answer A is true since we use the top function f(x) = -x + 1 since the input is -1 which is less than 0 (x < 0). We check to make sure the equation comes out true:

f(-1) = -(-1) + 1

f(-1) = 2 ✓

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wagonbelleville wagonbelleville · Answer 2 · 2019-03-19T16:32:57+01:00

Answer:

The correct options are [tex]f(-1)=2[/tex] and [tex]f(1)=0[/tex].

Step-by-step explanation:

We are given the function,

[tex]\left\{\begin{matrix}-x+1&x<0\\-2&x=0\\x^2-1&x>0\end{matrix}\right[/tex].

Now, according to the options, we have,

When x= -1 and x= -2, the function is [tex]f(x)=-x+1[/tex].

Then, [tex]f(-1)=-(-1)+1=1+1=2[/tex]

Also, [tex]f(-2)=-(-2)+1=2+1=3[/tex]

When x= 1 and x= 4, the function is [tex]f(x)=x^2-1[/tex]

Then, [tex]f(1)=1^2-1=1-1=0[/tex]

Also, [tex]f(4)=4^2-1=16-1=15[/tex]

Thus, the correct options are [tex]f(-1)=2[/tex] and [tex]f(1)=0[/tex].