Question

Identify the function shown in the graph.

Options

• sin^–1 x

• sin^–1 (2x)

• `sin^-1(x/2)`

• 2 sin^–1 x

Answer 1

sin^–1 (2x)

Explanation:

From graph

For x = `-1/2`, y = `-pi/2`

For x = 0, y = 0

For x = `1/2` y = `pi/2`

Let’s check options:

1. sin^–1 x

Now, y = sin^–1 x

Putting x = `1/2`

y = `sin^(-1) (1/2)`

y = 30°

y = `pi/6`

Since y ≠ `1/2`, this is not correct.

2. sin^–1 (2x)

Now, y = sin^–1 (2x)

Putting x = `1/2`

y = `sin^-1 (2 xx 1/2)`

y = sin^–1 (1)

y = 90°

y = `pi/2`

Since y = `1/2`, this is correct.

We don’t need to check other options.

So, the correct answer is sin^–1 (2x).