সংযোজিত ফংশন
f(x)= x−2 \sqrt{x - 2} x−2 এবং g(x)=x2+1 হলে fog এর ডোমেন কত ?
(-∞, -1] ∪ [1,∞)
[-1, 1]
(-∞, ∞)
(-∞, -1) ∪ (1, ∞)
Sol n:fog(x)=f(g(x))=f(x2+1)=x2+1−2=x2−1=(x−1)(x+1) [বুয়েট’ ১০-১১] ডোমেন fog: =(−∞,−1]∪[1,∞)∴ উ: (ক) \begin{array}{l}\text { Sol }^{n}: \mathrm{fog}(\mathrm{x})=\mathrm{f}(\mathrm{g}(\mathrm{x}))=\mathrm{f}\left(\mathrm{x}^{2}+1\right) \\ =\sqrt{\mathrm{x}^{2}+1-2}=\sqrt{\mathrm{x}^{2}-1} \\ =\sqrt{(\mathrm{x}-1)(\mathrm{x}+1)} \quad \text { [বুয়েট' ১০-১১] } \\ \text { ডোমেন fog: }=(-\infty,-1] \cup[1, \infty) \quad \therefore \text { উ: (ক) }\end{array} Sol n:fog(x)=f(g(x))=f(x2+1)=x2+1−2=x2−1=(x−1)(x+1) [বুয়েট’ ১০-১১] ডোমেন fog: =(−∞,−1]∪[1,∞)∴ উ: (ক)
If AAA and BBB have nnn elements in common, then the number of elements common to A×BA\times BA×B and B×AB\times AB×A is
If g(f(x))=∣sinx∣g(f(x))= |\sin x|g(f(x))=∣sinx∣ and g(f(x))=sin2x,g(f(x))= \sin ^2 \sqrt{x},g(f(x))=sin2x, then-
f(x)=x4–x2+14 f{\left ( x \right )} = x^{4} – x^{2} + \frac{1}{4} f(x)=x4–x2+41 এবং g(x)=x+1 g{\left ( x \right )} = \sqrt{x + 1} g(x)=x+1 হলে fog(x) = কত?
A function f:R→R f : R \rightarrow Rf:R→R satisfies x cos y (f (2x+2y)-f(2x-2y))=cos x sin y (f(2x+2y)+f(2x-2y)). If f′(0)=12f'(0)=\dfrac{1}{2}f′(0)=21, then-
