Question

If f, g, h are real functions given by $f\left(x\right)=x^2,g\left(x\right)=tanx$ and $h\left(x\right)=lo{g}_{e}x$, then write the value of $hogof\left(\sqrt{\frac{\pi }{4}}\right)$

Answer 1

We have,
$f\left(x\right)=x^2,g\left(x\right)=tanx$
and $h\left(x\right)=lo{g}_{e}x$
Now,
$\left(hogof\right)\left(\sqrt{\frac{\pi }{4}}\right)=h\left[g\right(f\left)\right]\left(\sqrt{\frac{\pi }{4}}\right)=h\left[g\left(\sqrt{\frac{\pi }{4}}\right)\right]=h\left[tan\frac{\pi }{4}\right]=h\left(1\right)=lo{e}_{e}1=0$