The domain of function ^ -1 (2 x-3) is : - Vidyadip

Question

The domain of function $\cos ^{-1}(2 x-3)$ is :

✓

Answer

(D)
The domain of $\cos ^{-1}(\theta)$ is $-1 \leq \theta \leq 1$$
\begin{array}{ll}
\text { So, } & -1 \leq 2 x-3 \leq 1 \\
\Rightarrow & -1+3 \leq 2 x-3+3 \leq 1+3 \\
\Rightarrow & 2 \leq 2 x \leq 4 \\
\Rightarrow & 1 \leq x \leq 2 \\
\Rightarrow & x \in[1,2]
\end{array}
$
Hence correct option is (D).

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Inverse Trigonometric Functions→Inverse Trigonometric Functions — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Linear programming model which involves funds allocation of limited investment is classified as:

Ordination budgeting model
Capital budgeting models
Funds investment models
Funds origin models.

Let $[x]$ denote the greatest integer less than or equal to $x$. If $f(x) = \sin^{-1}x, g(x) = [x^2]$ and $\text{h(x)}=2\text{x},\frac{1}{2}\leq\text{x}\leq\frac{1}{\sqrt{2}},$ then

Choose the correct answer from the given four options: The area of the region bounded by the curve $x^2 = 4y$ and the straight line $x = 4y - 2$ is:

If $\vec{\text{a}}=2\hat{\text{i}}-3\hat{\text{j}}-\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}+4\hat{\text{j}}-2\hat{\text{k}},$ then $\vec{\text{a}}\times\vec{\text{b}}$ is:

$10\hat{\text{i}}+2\hat{\text{j}}+11\hat{\text{k}}$
$10\hat{\text{i}}+3\hat{\text{j}}+11\hat{\text{k}}$
$10\hat{\text{i}}-3\hat{\text{j}}+11\hat{\text{k}}$
$10\hat{\text{i}}-2\hat{\text{j}}-10\hat{\text{k}}$

Let $f, g : R \rightarrow R$ be defined by $f(x) = 3x + 1$ and $g(x) = x^2 - 2, \forall x \in R,$ respectively. Then, $\text{fog}$ is:

Choose the correct answers from the given four options: The function $\text{f(x)}=\text{e}^{|\text{x}|}$ is:

If $\alpha, \beta, \gamma$ are the direction angles of a vector and $\cos \alpha=\frac{14}{15}, \cos \beta=\frac{1}{3}$, then $\cos \gamma=$

If $\hat{i}, \hat{j}, \hat{k}$ are unit vectors along three mutually perpendicular directions, then

The vector equation of the plane containing the line $\vec{\text{r}}=(-2\hat{\text{i}}-3\hat{\text{j}}+\hat{\text{k}})+\lambda(3\hat{\text{i}}-2\hat{\text{j}}-\hat{\text{k}})$ and the point $\hat{\text{i}}+2\hat{\text{j}}+3\hat{\text{k}}$ is:

$\vec{\text{r}}.(\hat{\text{i}}+3\hat{\text{k}})=10$
$\vec{\text{r}}.(\hat{\text{i}}-3\hat{\text{k}})=10$
$\vec{\text{r}}.(3\hat{\text{i}}+\hat{\text{k}})=10$
$\text{None of these}$

Fifteen coupons are numbered 1 to 15. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is 9 is:

$\big(\frac{3}{7}\big)^7$
$\big(\frac{1}{15}\big)^7$
$\big(\frac{8}{15}\big)^7$
$\text{None of these}$