Let yfxyfx be the piecewise defined function given below Let

Let y=f(x)y=f(x) be the piecewise defined function given below.

Let y = f(x) be the piecewise defined function given below. f(x) = -x - 1, 1, x - 1 f(-3)= f(2) = For what values of x is f(x) = 1? Find the domain and range of f. (You may find it helpful to graph this function on your own paper to find the domain and range.) Your answers must be inequalities (not intervals).

Solution

a) f(-3)

for values less than -2 , f(x) = -x -1

==> f(-3) = -(-3) -1 = 3 - 1

==> f(-3) = 2

b) f(2)

for the value x = 2 , f(x) = x -1

==> f(2) = 2 -1 = 1

c) f(x) = 1 for values between -2 and 2

and f(2) = 1 , f(-2) = 1

Hence f(x) = 1 for [-2 , 2] ==> -2 <= x <= 2

d) Domain

function is defined for all x

==> Domain of f(x) = (- , ) ==> - < x < -

Range

for any x , function value is greater than or equal to 1

==> Range of f(x) is 1 <= x < ==> [1 , )