Question

Why is the answer B? Plz explain.

Answer 1

Given f(x)=|x-2|-3

f(0) = |0-2|-3 = |-2| -3 = 2-3 = -1

So we need to solve f(a) = |x-2| = -1

Solving an absolute value problem is like having two equations,

(x-2)-3 = -1..................(1), and

-(x-2)-3 = -1................(2)

Solving (x-2)-3 = -1 => x=-1+2+3 = 4

Solving -(x-2)-3 = -1 => -x+2-3 = -1 => x=2-3+1=0 which is our previous answer.

So from the solution of x = 4, we note that 4>0, this means a=4.

Answer 2

Oh I see. You wonder why f(0) and f(4) are equal.

f(4) = |x - 2| - 3 = |4 - 2| - 3 = |2| - 3

The absolute value of 2 does not change so it is really 2 - 3 = -1

f(0) = |0 - 2| - 3 = | - 2| - 3 = 2 - 3 = - 1 The absolute value of minus 2 is plus two.

No other value will do what f(0) does with f(4)

Try A for example

f(3) = |3 - 2| - 3 = |1| - 3 = 1 - 3 = - 2 which is not minus 1.

Lastly we'll look at D.

f(6) = |6 - 2| - 3 = 4 - 3 = 1 not - 1.

Conclusion a = 4 and f(0) = f(4)

B <<<<< Answer.