Which integers have an absolute value of 45?

Answer 1

f(x) = abs(x), the "absolute value"-funtion is the function defined as follows:

f(x) = x iff x>=0 and f(x) = -x if x<0.

We are asked to solve f(x) = 45, hence:

if x>=0 then f(x) = x = 45

if x<0 then f(x) = -x = 45 iff x = -45.

So, the answer is: 45 and -45.

But only because 45 and -45 are indeed integers.

If the question had been which numbers have an absolute value of 45, then we can include the complex numbers. We will then arrive at all numbers lying on the circle with radius 45.

f(x) will take another form for complex numbers:

f(x) = (Re(x)^2 + Im(x)^2)^(1/2).