XAT 2022 — QA & DI Question 28
Read the following scenario and answer the THREE questions that follow.
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The given candlestick chart depicts the prices of a particular stock over 10 consecutive days. A candlestick comprises of a rectangular box pieced by a line. The top and bottom ends of the line respectively indicate the maximum and minimum prices of the stock on that day, while the horizontal edges of the rectangle correspond to the stock's opening and closing prices. If the rectangle is white, the opening price is lower than the closing price, but if the rectangle is black, then it is the other way around.
Using the above information, answer the questions that follow:
Consider the real-valued function f(x) = . Find the domain of f(x).
Answer & solution
- B
R -
- C
R -
- D
R -
- E
The function f(x) = is only defined when both the numerator and the denominator of the function are defined are the denominator is not equal to zero.
The logarithm of the function is only defined for positive values :
Hence 3x - 7 is greater than zero. Hence x > 7/3.
The value inside square root are defined for positive values. The value of the quadratic equation in the square root must be positive.
Hence 2x2 - 7x + 6 = 0 has the roots:
, : 2, 3/2
The quadratic equation is positive for:
∪ (2, ∞)
Since in order to be a part of the domain the values of x must be greater than 7/3 and 7/3 is greater than 2 all values of x which are greater than 7/3 must be a part of the domain for x.