`"If "f:R to R, g:R and h:R to R` be three functions are given by `f(x)=x^(2)-1,g(x)=sqrt(x^(2)+1)and h(x)={{:(,0,x le0),(,x,xgt 0):}` Then the composite functions (ho fog) (x)) is given byA. `{{:(,-x^(2),x lt 0),(,0,x=0),(,x^(2),x gt0):}`B. `{{:(,x^(2),xne0),(,0,x=0):}`C. `{{:(,x^(2),xgt 0),(,0,xle0):}`D. None of these

`"If "f:R to R, g:R and h:R to R` be three functions are given by `f(x

1.	`"If "f:R to R, g:R and h:R to R` be three functions are given by `f(x)=x^(2)-1,g(x)=sqrt(x^(2)+1)and h(x)={{:(,0,x le0),(,x,xgt 0):}` Then the composite functions (ho fog) (x)) is given byA. `{{:(,-x^(2),x lt 0),(,0,x=0),(,x^(2),x gt0):}`B. `{{:(,x^(2),xne0),(,0,x=0):}`C. `{{:(,x^(2),xgt 0),(,0,xle0):}`D. None of these
Answer» Correct Answer - B We have, `("ho fog")(x)=h("fog (x)")=h(f(g(x))=h(f(sqrt(x^(2)+1))` `("ho fog")(x)=h(x^(2)+1-1)=h(x^(2))` `Rightarrow ("ho fog")(x)={{:(,x^(2),x^(2)ne0),(,0,x=0):}`