If f (x) = tan x, −π2<x<π2 and g (x) = 1−x2−−−−−√ , then domain of fog is
fog(x)=f(g(x))=f(1−x2−−−−−√)⇒fog(x)=tan1−x2−−−−−√
and it is defined if
1−x2≥0⇒x2≤1⇒−1≤x≤1
f(x)−−−−√ is defined only if
f(x)will be non negative.
Hence ∴−f(x)−−−−−√is defined only for 0.
Let z=π9−x2−−−−−−√ and it is defined if
π9−x2≥0⇒x2≤π9
∴0≤z≤π3
∴0≤tanz≤3–√