Let f(x) and g(x) be two real polynomials of degree 2 and 1 respectively. If f(g(x)) = 8x2 – 2x and g(f(x)) = 4x2 + 6x + 1, then the value of f(2) + g(2) is ____________ .
For real number a, b (a > b > 0), let\(\text{{Area}} \left\{ (x, y) : x^2 + y^2 \leq a^2 \text{{ and }} \frac{x^2}{a^2} + \frac{y^2}{b^2} \geq 1 \right\} = 30\pi\)and \(\text{{Area}} \left\{ (x, y) : x^2 + y^2 \geq b^2 \text{{ and }} \frac{x^2}{a^2} + \frac{y^2}{b^2} \leq 1 \right\} = 18\pi\)Then the value of (a – b)2 is equal to _____.
Let\(f(x)=\frac{x−1}{x+1},x∈R− \left\{0,−1,1\right\}\)If ƒn+1(x) = ƒ(ƒn(x)) for all n∈N, then ƒ6(6) + ƒ7(7) is equal to :
Let\(A = \{z \in \mathbb{C} : |\frac{z+1}{z-1}| < 1\}\)and\(B = \{z \in \mathbb{C} : \text{arg}(\frac{z-1}{z+1}) = \frac{2\pi}{3}\}\)Then \(A∩B\) is :
\(\lim_{{x \to \frac{1}{\sqrt{2}}}} \frac{\sin(\cos^{-1}(x)) - x}{1 - \tan(\cos^{-1}(x))}\)is equal to :
g :R→R be two real valued functions defined as\(f(x) = \begin{cases} -|x + 3| & x < 0 \\ e^x, & x \geq 0 \end{cases}\)and\(g(x) = \begin{cases} x^2 + k_1x ,& x < 0 \\ 4x + k_2 ,& x \geq 0 \end{cases}\)where k1 and k2 are real constants. If (goƒ) is differentiable at x = 0, then (goƒ) (–4) + (goƒ) (4) isequal to:
Let S be the set of all the natural numbers, for which the line \(\frac{x}{a}+\frac{y}{b}=2 \)is a tangent to the curve\((\frac{x}{a})^n+(\frac{y}{b})^n=2 \)at the point (a, b), ab ≠ 0. Then :
The area bounded by the curve \(y=|x^2−9| \)and the line y = 3 is