Find the domain restriction for the function f (x) = (2x-5) ^4. Use an inequality to State the domain.

Question

Mathematics

Spunky

11 March, 04:32

Find the domain restriction for the function f (x) = (2x-5) ^4. Use an inequality to State the domain.

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Answers (1)

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Savanah Wolfe · Answer 1

On function f (x) there is no domain restriction all real numbers are in the domain of f (x).

Step-by-step explanation:

x∈R (set of all real numbers)

or in other words we can write the domain of x as - ∞
Given equation: f (x) = (2x-5) ^4

when;

x=-2: f (-2) = (2 (-2) - 5) ^4 = (-4-5) ^4 = (-9) ^4 = [ (-1) ^4]*[ (9) ^4] = (9) ^4=6561

x=-1: f (-1) = (2 (-1) - 5) ^4 = (-2-5) ^4 = (-7) ^4 = [ (-1) ^4]*[ (7) ^4] = (7) ^4=2401

x=0: f (0) = (2 (0) - 5) ^4 = (0-5) ^4 = (-5) ^4 = [ (-1) ^4]*[ (5) ^4] = (5) ^4=625

x=1: f (1) = (2 (1) - 5) ^4 = (2-5) ^4 = (-3) ^4 = [ (-1) ^4]*[ (3) ^4] = (3) ^4=81

x=2: f (1) = (2 (2) - 5) ^4 = (4-5) ^4 = (-1) ^4 = 1

The value of given function is decreasing rapidly when the value of x increases.