Let f(x) be the derivative of tan-1xx2+1+1 for all x∈R&g(x)=1f(x)+1fx2; for all x∈R. Let h-1(x) represent inverse function of h(x) then, which of the following is (are) TRUE?

f(x)=ddxtan−1⁡xx2+1+1 Let x=tan⁡θ⇒θ∈−π2,π2tan−1⁡tan⁡θsec⁡θ+1=tan−1⁡tan⁡θ2⇒θ2=tan−1⁡x2⇒f(x)=121+x2g(x)=1f(x)+1fx2=21+x2+21+x4=2x4+x2+2 Range _:[4,∞) Since g is many one g−1 does not exists.