SOLUTION: {{{ Let f(x) }}} = {{{ 1/(x+6) }}} and {{{ g(x) = 6x/(x+6) }}} Find domain of: {{{ f(x)+g(h) }}} = {{{ f(x) - g(x) }}} = {{{ f(x) * g(x) }}} = {{{ f(x)/g(x) }}}

Algebra ->  Functions -> SOLUTION: {{{ Let f(x) }}} = {{{ 1/(x+6) }}} and {{{ g(x) = 6x/(x+6) }}} Find domain of: {{{ f(x)+g(h) }}} = {{{ f(x) - g(x) }}} = {{{ f(x) * g(x) }}} = {{{ f(x)/g(x) }}}       Log On


   

Question 906111: +Let+f%28x%29+ = +1%2F%28x%2B6%29+ and +g%28x%29+=+6x%2F%28x%2B6%29+

Find domain of:
+f%28x%29%2Bg%28h%29+ =
+f%28x%29+-+g%28x%29+ =
+f%28x%29+%2A+g%28x%29+ =
+f%28x%29%2Fg%28x%29+ =

Thank you
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
+Let+f%28x%29+ = +1%2F%28x%2B6%29+ and +g%28x%29+=+6x%2F%28x%2B6%29+

Find domain of:
+f%28x%29%2Bg%28h%29++=+1%2F%28x%2B6%29%2B6x%2F%28x%2B6%29=+%281%2B6x%29%2F%28x%2B6%29+
since denominator cannot be equal to zero, exclude value of x that makes x%2B6=0 => for x=-6 denominator will be equal to zero
so, domain is: { x element R : x%3C%3E-6 }

+f%28x%29+-+g%28x%29++=+1%2F%28x%2B6%29-6x%2F%28x%2B6%29=+%281-6x%29%2F%28x%2B6%29+++
domain is same as above: { x element R : x%3C%3E-6 }

+f%28x%29+%2A+g%28x%29+=+1%2F%28x%2B6%29%2A6x%2F%28x%2B6%29+=++6x%2F%28x%2B6%29%5E2+
%28x%2B6%29%5E2=0 for x=-6
so,domain is same as above: { x element R : x%3C%3E-6 }


here we also have denominator x%2B6, so exclude x=-6 like above
than we got denominator 6x that will be equal to zero if x=0,exclude this one too
so, domain is: { x element R : x%3C%3E-6 and x%3C%3E0 }