BITSAT 2025 | Functions Question 1 | Mathematics

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

$\left[-\frac{\pi}{2}+\theta, \frac{\pi}{2}+\theta\right]$

$[\pi-\theta, \pi+\theta]$

$\left[-\frac{\pi}{2}-\theta, \frac{\pi}{2}-\theta\right]$

$\left[2 \pi-\frac{\theta}{2}, \frac{\pi}{2}+\theta\right]$

BITSAT 2025

MCQ (Single Correct Answer)

-1

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

$\{-5,9\}$

$\{0,-5\}$

$\{0,9\}$

$\{0,2\}$

BITSAT 2024

MCQ (Single Correct Answer)

-1

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

-2

-1

BITSAT 2023

MCQ (Single Correct Answer)

-1

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

$$x-2$$

$$x+2$$

$$-x-2$$

$$-x+2$$

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