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denpristay [2]
2 years ago
9

Select all the correct answers

Mathematics
1 answer:
brilliants [131]2 years ago
5 0

Answer:

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

Step-by-step explanation:

Given functions are,

f(x) = x^{\frac{1}{3} }

h(x) = (2x)^\frac{1}{3}+5

Option (1)

y-intercept of function 'h',

x = 0,

h(x) = (0)^\frac{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)^\frac{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.

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