Functions · Mathematics · BITSAT

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

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 $$f(x)=x^2-2 x+1$$ 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

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

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

Find the area enclosed by the loop in the curve 4y² = 4x² $$-$$ x³.

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

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 :

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

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

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