London is standing in a stadium and has the option of running up a staircase or down a staircase for exercise. The function f(x)=\frac{1}{25}\big(\left|6x\right|+4x\big)f(x)= 25 1 (∣6x∣+4x) will determine how many calories London will burn if she runs up xx steps. Use a negative value for xx if she runs down the stairs. Find and interpret the given function values and determine an appropriate domain for the function.

Question

13-10-2021
Mathematics

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London is standing in a stadium and has the option of running up a staircase or down a staircase for exercise. The function f(x)=\frac{1}{25}\big(\left|6x\right|+4x\big)f(x)= 25 1 (∣6x∣+4x) will determine how many calories London will burn if she runs up xx steps. Use a negative value for xx if she runs down the stairs. Find and interpret the given function values and determine an appropriate domain for the function.

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MrRoyal MrRoyal · Answer 1 · 2021-10-25T11:35:30+02:00

The domain of a function is the set of input values, the function can take.

The domain of the function is: [tex]\mathbf{(-\infty,\infty)}[/tex]

The function is given as:

[tex]\mathbf{f(x) = \frac{1}{25}\big(\left|6x\right|+4x\big)}[/tex]

The above function represents the number of steps she runs or up down from her current position.

Because she can move in either directions (i.e. up or down), then it means that, the domain of the function is: [tex]\mathbf{(-\infty,\infty)}[/tex]