What is the x-intercept for the piecewise function #f(x) = x^2-4 , x≥2# and #x-2, x<2#?

1 Answer
Nov 10, 2015

The x-intercept is at #x=2#

Explanation:

An x-intercept of a function #f(x)# is a point at which #f(x) = 0#
So, to find the x-intercepts, we look for what values of #x#, if any, fulfill this requirement.

For #x>=2# we have #f(x) = x^2 - 4 = (x+2)(x-2)#

#(x+2)(x-2) = 0 <=> x = -2 or x = 2#

But #-2 < 2# so the only x-intercept for #x >= 2# is at #x=2#

Finally we check for #x<2#

If #x < 2# we have #f(x) = x - 2 = 0 <=> x = 2#

But #2=2# and so there are no x-intercepts where #x < 2#

Thus the only x-intercept of #f(x)# occurs at #x = 2#.