Functions

If the function $f: R \rightarrow R$ is defined by $f(x)=x^2+5 x+9$, then $f^{-1}(9)$ is equal to

If $f: X \rightarrow Y$ be a function defined by $f(x)=a \sin \left(x+\frac{\pi}{4}\right)+b \cos x+c$ and $f$ is bijective, then the set $X$ with $\theta=\tan ^{-1}\left(\frac{a+\sqrt{2} b}{a}\right)$ is

Let $ [x] $ denote the greatest integer $ \leq x $. If $ f(x)=[x] $ and $ g(x)=|x| $, then the value of $ f\left(g\left(\frac{8}{5}\right)\right)-g\left(f\left(-\frac{8}{5}\right)\right) $ is

If \(f(x)=x^2-2 x+1\) and \(f \circ g(x)=x^2+2 x+1\), then \(g(x)\) is equal to

If g(x) = x2 + x \(-\) 2 and \(\frac{1}{2}gof(x)=2x^2-5x+2\), then f(x) is equal to

Find the area enclosed by the loop in the curve 4y2 = 4x2 \(-\) x3.

The maximum value of the function y = x(x \(-\) 1)2, is

If f(x) = 4x \(-\) x2, x\(\in\)R, and f(a + 1) \(-\) f(a \(-\) 1) = 0, then a is equal to

Let \(f(x) = {x \over {\sqrt {1 + {x^2}} }}\), \(\underbrace {fofofo.....of(x)}_{x\,times}\) is

The solution set of \({{|x - 2|\, - 1} \over {|x - 2|\, - 2}} \le 0\) is

\(\left\{ {x \in R:{{2x - 1} \over {{x^3} + 4{x^2} + 3x}} \in R} \right\}\) is equal to

Let f(x) = x \(-\) 3, g(x) = 4 \(-\) x. Then the set of values of x for which \(|f(x) + g(x)|\, < \,|f(x)| + |g(x)|\) is true, is given by :

If \(2f(xy) = {(f(x))^x} + {(f(y))^x}\) for all \(x,y \in R\) and \(f(1) = a( \ne 1)\). Then \(\sum\limits_{k = 1}^n {f(k) = }\)