The domain of the function ^(-1)(2x - 3) is Option 1: [1,2] Option 2: [-1,1] Option 3: (1,2) Option 4: (-1,1)

Answer: [1,2]. Solution: The inverse cosine function ^(-1) only accepts inputs between -1 and 1 (inclusive). For ^(-1)(2x - 3) to be defined, the input must satisfy: -1 ≤ 2x - 3 ≤ 1 From the left inequality: -1 ≤ 2x - 3 -1 + 3 ≤ 2x 2 ≤ 2x 1 ≤ x From the right inequality: 2x - 3 ≤ 1 2x ≤ 1 + 3 2x ≤ 4 x ≤ 2 Combining both results: 1 ≤ x ≤ 2 Therefore, the domain is [1, 2].

Algebra

Relations & Functions

Easy

core

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

[1,2]

[-1,1]

(1,2)

(-1,1)

✅ Correct Option: 1

The inverse cosine function $\cos^{-1}$ only accepts inputs between $-1$ and $1$ (inclusive).

For $\cos^{-1}(2x - 3)$ to be defined, the input must satisfy:

$-1 \leq 2x - 3 \leq 1$

From the left inequality:

$-1 \leq 2x - 3$

$-1 + 3 \leq 2x$

$2 \leq 2x$

$1 \leq x$

From the right inequality:

$2x - 3 \leq 1$

$2x \leq 1 + 3$

$2x \leq 4$

$x \leq 2$

Combining both results:

$1 \leq x \leq 2$

Therefore, the domain is $[1, 2]$ .

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Which of the following is true on the basis of above diagram?

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Match the LIST-I with LIST-II

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	LIST-I Function		LIST-II Nature
A.	$f: R \to R, f(x) = \sin^2 x + \cos^2 x$	I.	Bijective
B.	$f: Z \to Z, f(x) = x^3$	II.	Surjective but not injective
C.	$f: R \to R, f(x) = x^3 - x$	III.	Injective but not surjective
D.	$f: R \to R, f(x) = 3 - 4x$	IV.	Neither injective nor surjective

Choose the correct answer from the options given below:

The domain of the function cos⁡−1(2x−3)\cos^{-1}(2x - 3)cos−1(2x−3) is

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