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If f(x)=1/x ,g(x)=1/(x^2), and h(x)=x^2,...

If `f(x)=1/x ,g(x)=1/(x^2),` and `h(x)=x^2`, then
(A) `f(g(x))=x^2,x!=0,h(g(x))=1/(x^2)`
(B) `h(g(x))=1/(x^2),x!=0,fog(x)=x^2`
(C) `fog(x)=x^2,x!=0,h(g(x))=(g(x))^2,x!=0`
(D) none of these

A

`fog(x)=x^(2),x ne 0, h(g(x))=(1)/(x^(2))`

B

`h(g(x))=(1)/(x^(2)),x ne 0, fog(x)=x^(2)`

C

`fog(x)=x^(2), x ne 0, h(g(x))=(g(x))^(2), x ne 0`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x)=(1)/(x), g(x)=(1)/(x^(2)), and h(x)=x^(2)`
`f(g(x))=x^(2), x ne 0`
`h(g(x))=(1)/(x^(4))=(g(x))^(2), x ne 0`
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