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Select all the correct answers

Select all the correct answers-example-1
User York Wang
by
8.0k points

1 Answer

12 votes

Answer:

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.

User Nickolayratchev
by
8.6k points

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