Question

If $f\left(x\right)=si{n}^{2}x,g\left(x\right)=\sqrt{x}$ and $h\left(x\right)=co{s}^{-1}x,0\le x\le 1,$ then

• A. hogof(x) = gofoh(x)
• B. gofoh(x) = fohog(x)
• C. fohog(x) = hogof(x)
• D. None of these

Answer 1

The correct option is D

None of these

$hogof\left(x\right)=co{s}^{-1}\left(\sqrt{si{n}^{2}x}\right)=co{s}^{-1}\left(sinx\right)=\frac{\pi }{2}-xgofoh\left(x\right)=\sqrt{si{n}^2\left(co{s}^{-1}x\right)}=\sqrt{1-x^2}fohog\left(x\right)=si{n}^2\left(co{s}^{-1}\sqrt{x}\right)=1-x.$

Thus no two composites are equal.