Question

Select all the correct answers

Answer 1

Options (1), (2), (3), (6)

Explanation:

Given functions are,

f(x) =
`x^{(1)/(3) }`

h(x) =
`(2x)^(1)/(3)+5`

Option (1)

y-intercept of function 'h',

x = 0,

h(x) =
`(0)^(1)/(3)+5`

= 5

So y-intercept is (0, 5)

True.

Option (2)

Domain of function 'h' is (-∞, ∞)

True

Option (3)

As x approaches ∞, h(x) approaches ∞.

True.

Option (4)

For x intercept,

h(x) = 0

`(2x)^(1)/(3)+5=0`

2x = (-5)³

2x = -125

x = -62.5

So the x-intercept is (-62.5, 0)

False.

Option (5)

Range of the function 'h' is (-∞, ∞)

False

Option (6)

As x approaches to -∞, h(x) approaches to -∞.

Since, range of the function is (-∞, ∞), given statement is true.

Therefore, Options (1), (2), (3), (6) are correct.