Hello!
We will have three possible functions, according to the value of x, look:
if x = 0:
f(x) = -2
if x < 0:
f(x) = -x +1
if x > 0:
f(x) = x² -1
Knowing it, let's analyze each statement:
A. f(-1) = 2
f(-1) = -x +1
f(-1) = -(-1) +1
f(-1) = 1+1
f(-1) = 2
TRUE
B. f(-2) = 0
f(-2) = -x +1
f(-2) = -(-2) +1
f(-2) = 2 +1
f(-2) = 3
FALSE
C. f(4) = 7
f(4) = x² +1
f(4) = 4² +1
f(4) = 16 +1
f(4) = 17
FALSE
D. f(1) = 0
f(1) = x² +1
f(1) = 1² +1
f(1) = 1 +1
f(1) = 2
FALSE