I need help solving this....

Find the domain of the composite function f*g

f(x)=Radical x-2 (x-2 is the radicand)

g(x)=2/x-10

The answer is x|10I know how the problem came to the answer of 10, but not 11. Can someone please show me?? Easy 10 points!!!

## Answers (1)

hmm....f(x) = √ ( x - 2) ...but is g(x) = [ 2 / x ] - 10 or 2 / [ x - 10 ]...answer implies the latter

f(g(x)) = √ ( 2 / [ x - 10 ] - 2 ) = √ ( [ 22 - 2x ] / [ x - 10 ] )...what is under the radical must be ≥ 0

which implies x in ( 10 , 11 ]...to solve the ≥ the key values are x = 10 & 11

if x < 10 the quantity is < 0 , if x > 11 the quantity is also < 0...inequality work