MCQ
If $g(f(x)) = |\sin x|$ and $f(g(x)) = {(\sin \sqrt x )^2}$, then
- ✓$f(x) = {\sin ^2}x,\;g(x) = \sqrt x $
- B$f(x) = \sin x,\;g(x) = |x|$
- C$f(x) = {x^2},\;g(x) = \sin \sqrt x $
- D$f$ and $g$ cannot be determined
✓
Answer
Correct option: A.
$f(x) = {\sin ^2}x,\;g(x) = \sqrt x $
a
(a) $g\,\left\{ {f(x)} \right\} = \,|\sin x|,\,\,f\left\{ {g(x)} \right\} = {(\sin \sqrt x )^2}$
(a) $g\,\left\{ {f(x)} \right\} = \,|\sin x|,\,\,f\left\{ {g(x)} \right\} = {(\sin \sqrt x )^2}$
Considering $f(x) = {\sin ^2}x,\,\,g(x) = \sqrt x ,$ then
$g\,[f(x)] = g\,({\sin ^2}x) = \sqrt {{{\sin }^2}x} = \,\,|\sin x|$
$f[g(x)] = f[\sqrt {x]} = {(\sin \sqrt x )^2}$.
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