Determine the value of the variable for which the expression is defined as real number. (1x2−2x−63)12

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Determine the value of the variable for which the expression is defined as real number.  (1x2−2x−63)12

Adnaan Franks · Accepted Answer

Given: (1x2−2x−63)12 Solution: (1x2−2x−63)12 By using the exponent property an=a1n The given expression written as (1x2−2−63)12=1x2−2x−63 Since it is a square root function. So, the function will be defined fot the x - values for which the term inside the radical sign is greater than or equal to 0. So, find the values of variable for which the expression is defined as real number. Now solve inequality 1x2−2x−63≥0 1(x−9)(x+7)≥0 So, the critical points occur at x=9 and x=−7 So, check the inequality on the intervals (−∞,7),(−7,9) and (9,∞) And see where there inequality holds true. On interval, (−∞,−7) take the rest point x=−8 1(−8)2−2(−8)−63≥0 117≥0 Therefore, true statement. On the interval (-7,9) take the rest point x=0 1(0)2−2(0)−63≥0 −163≥0 False statement On the interval (9,∞) take the rest point x=10 1(10)2−2(10)−63≥0 117≥0 Therefore, true statement Thus, the values of the variables for which the expression is defined as a real number occur in the interval (−∞,−7)∪(9,∞)

Determine the value of the variable for which the expression is defined as real

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