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If the functions f, g and h are defined ...

If the functions f, g and h are defined from the set of real numbers R to R such that
`f(x)=x^(2)-1,g(x)=sqrt((x^(2)+1))`,
`h(x)={{:("0,","if",x<0),("x,","if",xge0):}`
Then find the composite function ho(fog)(x).

A

`{{:(,-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

Text Solution

Verified by Experts

The correct Answer is:
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):}`
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