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Question

If the functions f,g and h are defined from the set of real numbers RR such that fx=x2-1, gx=x2+1 and hx=0,ifx0x,ifx0 then hfgx is defined by


A

1

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B

0

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C

-1

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D

x2

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Solution

The correct option is D

x2


Explanation for the correct option:

The given functions are fx=x2-1, gx=x2+1 and hx=0,ifx<0x,ifx0.

Thus, hfgx=hfgx

hfgx=hfx2+1[gx=x2+1]hfgx=hx2+12-1[fx=x2-1]hfgx=hx2+1-1hfgx=hx2

As x20, thus hx2=x2.

Therefore, hfgx=x2.

Hence, option (D) is the correct answer.


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