IfF(x)= -3x if x < -1 0 if x = -1 2x^2+1 if x > -1 Find (a) f(-2) (b) f(-1) (c) f(0)

If F(x)=-3x if x < -1
0 if x = -1
$2{x}^{2}+1$ if x > -1
Find (a) f(-2) (b) f(-1) (c) f(0)
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Urijah Hahn
In order to solve this function, you have torealize that this function has three different conditions for whichx can affect F(x). Hence why F(x) equals to three differentproblems. Depending on what your x equals to, you have to use the proper F(x) that matches the condition of your particular x.
So for (a):
F(-2) = F(x) equals to what when x = -2?
One of the conditions is F(x) = -3x when x < -1
So in that case, since your x = -2 is less than -1, your F(x)= -3x or really F(-2) = -3(-2) = 6
Same rules apply for (b) and (c):
(b) F(-1), F(x) = 0 if x = -1 and x = -1, therefore F(-1) = 0
(c) F(0), $F\left(x\right)=2{x}^{2}+1$ if x > -1 and x = 0, therefore $F\left(0\right)=F\left(x\right)=2\left(0{\right)}^{2}+1=1$
In conclusion: (a) = 6, (b) = 0 and (c) = 1