Solving Logarithmic Functions Quiz

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In the given text, the function f(x) = log(x - 1) - log(x - 2) is defined for values of x such that ___.

x > 2 (correct)

x > 3

x > 1

Based on the text, which type of function is f(x) = x + |x|?

Injective

Bijective

None of these (correct)

Surjective

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))?

-1

2

1 (correct)

4

Which of the following functions is not homogeneous?

$y^2 + x^2 + y^3$ Signup and view all the answers

For which interval does the function g(x) = log(x-1) - log(x-2) hold true?

$(2, +\infty)$ Signup and view all the answers

Which of the following functions can be classified as an implicit function?

$5xy + 2x - y + 1$ Signup and view all the answers

What is the range of the function f(x) = cos(2x) (sec(2x) + 2 tan(x))?

[0, 2) 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?

0 < c ≤ 1 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)?

(-∞, ∞) 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?

a > 2 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))?

(0, ∞) 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)?

3 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?

There is no value of $a$ that makes the function one-to-one. Signup and view all the answers

What is the value of the expression $2[x] + 2/[x] - 1$ if $[x] = -1$?

4 Signup and view all the answers

What is the graph of the function $f(x) = \max{1 + x, 1 - x, 2}$?

A piecewise linear function with three linear segments Signup and view all the answers

Which of the following functions is homogeneous?

$f(x, y) = x^2 - y^2$ Signup and view all the answers

What is the period of the function $f(x) = 2 \sin(3x) + 4 \cos(5x)$?

$\frac{2\pi}{5}$ Signup and view all the answers

What is the domain of the logarithmic function $f(x) = \log_2(x - 3)$?

$x > 3$ Signup and view all the answers