If f(x) is continuous and increasing functin such that the domain of `g(x) = sqrt(f(x)-x)` be R and `h(x) =(1)/(1-x)` then the domain of `phi(x)=sqrt(f(f(f(x)))-h(h(h(x))))`is -

Options

A. R
B. {0,1}
C. R-{0,1}
D. `R^(+)-{1}`

Answer

3

Explanation

`h(x) = (1)/(1-x), x ne 1 rArr h(h(x)) = (x-1)/(x),x ne 0,1`
`"also",g(x)ge f(x)0 x epsilion R`
`rArr f(f(f(x)))ge1(x)gex`
`rArr f(f(f(x)))-xge0`
`therefore phi (x) "is defined for all" x epsilon R- {0,1}.`