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 · 2019-03-19T11:32:57-04:00

Answer:

The correct options are \(f(-1)=2\) and \(f(1)=0\).

Step-by-step explanation:

We are given the function,

\(\left\{\begin{matrix}-x+1&x<0\\-2&x=0\\x^2-1&x>0\end{matrix}\right\).

Now, according to the options, we have,

When x= -1 and x= -2, the function is \(f(x)=-x+1\).

Then, \(f(-1)=-(-1)+1=1+1=2\)

Also, \(f(-2)=-(-2)+1=2+1=3\)

When x= 1 and x= 4, the function is \(f(x)=x^2-1\)

Then, \(f(1)=1^2-1=1-1=0\)

Also, \(f(4)=4^2-1=16-1=15\)

Thus, the correct options are \(f(-1)=2\) and \(f(1)=0\).