SOLUTION: Find the domain of {{{ h(x)=1/4th root(x^2-5x) }}} {{{ 4th root(x^2-5x) >or equal to 0 }}} {{{ x^2-5x >or equal to 0 }}} {{{ x(x-5) >or equal to 0 }}}

Algebra ->  Functions -> SOLUTION: Find the domain of {{{ h(x)=1/4th root(x^2-5x) }}} {{{ 4th root(x^2-5x) >or equal to 0 }}} {{{ x^2-5x >or equal to 0 }}} {{{ x(x-5) >or equal to 0 }}}      Log On


   

Question 335903: Find the domain of +h%28x%29=1%2F4th+root%28x%5E2-5x%29+
+4th+root%28x%5E2-5x%29+%3Eor+equal+to+0+
+x%5E2-5x+%3Eor+equal+to+0+
+x%28x-5%29+%3Eor+equal+to+0+
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the domain of h(x)= 4th root(x^2-5x)

x^2-5x >= 0
x(x-5) >= 0
---
Solve the equality:
x = 0 or x = 5
------------------------
To solve the inequality:
1st: Draw a number line and plot x = 0 and x = 5
2nd: Check a test-value from each of the three
resulting intervals to determine where the solutions
for the inequality lie.
-------------
x(x-5) > 0
Check x = -10: -*->0 ; true, so solutions in (-inf,0)
Check x = 2: +*->0 ; false, so no solutions in (0,5)
Check x = 10: +*+>0 ; true, so solutions in (5,+inf)
========================================================
Final solution:
[0,5] or 0<= x <=5
=================
Cheers,
Stan H.