Question

How do you do this? I’m really lost

Answer 1

Answer:

Step-by-step explanation:

To do these the main think to consider is the boundaries of the functions.  In other words, check when the boundary is true and use that function.  And so,

If we look at 1a.) f(-3) this means that x=-3.  Now check the boundary condition of both equations first.  For 6x-1 use it only if x<0 well is -3<0? Yes, so we will use this function.  But let's check why we won't use 7x+3 this is because the boundary is x≥0 and since x=-3, -3≥0 is false so we dont use that function.  Therefore:

f(x)=6x-1

f(-3)= 6(-3) - 1 = -18 - 1 = -19

1b.) Same idea so we will use 7x+3 because 0≥0 is true and so:

f(x)= 7x + 3

f(0) = 7(0) + 3 = 0 + 3 = 3

1c.) We will use the second equation since 4≥0 is true and so:

f(x) = 7x + 3

f(4) = 7(4) + 3 = 28 + 3 = 31

You will use the same logic to solve 2 and 3.  Good luck! Hope this helps!