Podcast
Questions and Answers
In the given text, the function f(x) = log(x - 1) - log(x - 2) is defined for values of x such that ___.
In the given text, the function f(x) = log(x - 1) - log(x - 2) is defined for values of x such that ___.
Based on the text, which type of function is f(x) = x + |x|?
Based on the text, which type of function is f(x) = x + |x|?
If f(x) is the greatest integer function and g(x) is the modulus function, then what is the value of g(−3/4) - f(g(−3/4))?
If f(x) is the greatest integer function and g(x) is the modulus function, then what is the value of g(−3/4) - f(g(−3/4))?
Which of the following functions is not homogeneous?
Which of the following functions is not homogeneous?
Signup and view all the answers
For which interval does the function g(x) = log(x-1) - log(x-2) hold true?
For which interval does the function g(x) = log(x-1) - log(x-2) hold true?
Signup and view all the answers
Which of the following functions can be classified as an implicit function?
Which of the following functions can be classified as an implicit function?
Signup and view all the answers
What is the range of the function f(x) = cos(2x) (sec(2x) + 2 tan(x))?
What is the range of the function f(x) = cos(2x) (sec(2x) + 2 tan(x))?
Signup and view all the answers
For what values of the constant c does the function f(x) = (x^2 + 2x + c)/(x^2 + x + c) attain all real values?
For what values of the constant c does the function f(x) = (x^2 + 2x + c)/(x^2 + x + c) attain all real values?
Signup and view all the answers
If f(x) = |x| + 1 for x ≤ 1 and f(x) = |x| - 1 for x > 1, what is the domain of f(x)?
If f(x) = |x| + 1 for x ≤ 1 and f(x) = |x| - 1 for x > 1, what is the domain of f(x)?
Signup and view all the answers
If f(x) = ax^2 + 6x - 8 and g(x) = a + 6x - 8x^2, what is the interval of values of a for which f is onto?
If f(x) = ax^2 + 6x - 8 and g(x) = a + 6x - 8x^2, what is the interval of values of a for which f is onto?
Signup and view all the answers
If f(x) = log_2(x+1) and g(x) = 2^x, what is the domain of f(g(x))?
If f(x) = log_2(x+1) and g(x) = 2^x, what is the domain of f(g(x))?
Signup and view all the answers
If f(x) = x^3 - 3x^2 + 2x and g(x) = x^2 - x, what is the degree of the homogeneous function f(x) + g(x)?
If f(x) = x^3 - 3x^2 + 2x and g(x) = x^2 - x, what is the degree of the homogeneous function f(x) + g(x)?
Signup and view all the answers
What is the value of the parameter $a$ that makes the given function $f(x) = x^2 + 3x + a$ one-to-one?
What is the value of the parameter $a$ that makes the given function $f(x) = x^2 + 3x + a$ one-to-one?
Signup and view all the answers
What is the value of the expression $2[x] + 2/[x] - 1$ if $[x] = -1$?
What is the value of the expression $2[x] + 2/[x] - 1$ if $[x] = -1$?
Signup and view all the answers
What is the graph of the function $f(x) = \max{1 + x, 1 - x, 2}$?
What is the graph of the function $f(x) = \max{1 + x, 1 - x, 2}$?
Signup and view all the answers
Which of the following functions is homogeneous?
Which of the following functions is homogeneous?
Signup and view all the answers
What is the period of the function $f(x) = 2 \sin(3x) + 4 \cos(5x)$?
What is the period of the function $f(x) = 2 \sin(3x) + 4 \cos(5x)$?
Signup and view all the answers
What is the domain of the logarithmic function $f(x) = \log_2(x - 3)$?
What is the domain of the logarithmic function $f(x) = \log_2(x - 3)$?
Signup and view all the answers
