Question
जाँच कीजिए कि के लिए
और
के लिए
।
Answer :
Word Count : 317
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मान लीजिए कि हमारे पास दो फलन हैं (f(x)) और (g(x))। हमें जांचना है कि [ (f \circ g)(x) = f(g(x)) = x \quad \text{और} \quad (g \circ f)(x) = g(f(x)) = x ] कुछ विशेष (x) के लिए। पहले (f \circ g) की जांच करते हैं। मान लें [ f(x) = \frac{x+1}{x-2}, \quad g(x) = \frac{2x+1}{x+1}. ] अब ((f \circ g)(x) = f(g(x))) निकालते हैं: [ f(g(x)) = f\left(\frac{2x+1}{x+1}\right) = \frac{\frac{2x+1}{x+1} + 1}{\frac{2x+1}{x+1} - 2}. ] साधारण भिन्नों को जोड़ते हैं: [ \frac{2x+1}{x+1} + 1 = \frac{2x+1 + x+1}{x+1} = \frac{3x+2}{x+1},
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जाँच कीजिए कि द्वारा दिया गया
सुपरिभाषित और 1-1 है। इसके आगे जाँच कीजिए कि किसी
के लिए
है।
Let (x1, x2, x3) and (y1, y2, y3) represent the coordinates with respect to the bases
,
. If
, find the representation of Q in terms of (y1, y2, y3).
द्वारा परिभाषित फलन
लीजिए:
Let V be the set of all functions that are twice differentiable in and
.
जाँच कीजिए कि किसी के लिए
है।
Write down the matrix of T on W w.r.t the basis S.