A) 3
B) 10
C) 13
D) 5
E) 0
Correct Answer: D
Solution :
We have, \[h(x)={{\{f(x)\}}^{2}}+{{\{g(x)\}}^{2}}\] On differentiating w.r.t.\[x,\]we get \[\Rightarrow \] \[h(x)=2f(x)f(x)+2g(x)g(x)\] ??(i) Now,\[f(x)=g(x)\]and\[f\,(x)=-f(x)\] \[\Rightarrow \] \[f\,(x)=g(x)\]and\[f\,(x)=-f(x)\] \[\Rightarrow \] \[-f(x)=g(x)\] Thus,\[f(x)=g(x)\]and\[g(x)=-f(x)\] From (i) \[h(x)=-2g(x)g(x)+2g(x)g(x)\] \[=0\] \[\Rightarrow \] \[h(x)=5\] \[[\because h(5)=5]\] \[\therefore \] \[h(10)=5\]You need to login to perform this action.
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