1. G

    How to find value of k to obtain self-inverse of a function

    I get bogged down with this. Can someone offer a clue on how to go about it. Please see attached file. Thanks.
  2. O

    Quadratic word problem

    Hi, I hope someone can help me determine the quadratic equation for the following word problem: Note that below is question 1: I was easily able to develop the equation for question 1, which the question prompt for a linear equation, as follows: Now for question 2, I need to develop...
  3. O

    domain of combined function

    Hi, I hope someone can help. I'm trying to figure out the domain for the product of f(x) and g(x). f(x) = \log_{10}(x+3)^2 g(x) = \sqrt{x-1} I know that the domain for f(x) is x > -3 and the domain for g(x) is x \leq -1 or x \geq 1. According to my textbook the domain for the product of...
  4. A

    How to find the domain of this fumction?

    The function is f(x)=ln($x+\sqrt(x^2+1)$) Note- The square root is over the whole $x^2+1$
  5. A

    Why isn't the other part of the graph taken?

    The question is- Make the function $f:R\rightarrow$$R$, $f(x)=x^2$ invertible by making suitable adjustments to the domain and range. So, here is what my teacher said- Since we have to make the function onto, we must make the range equal to co-domain. Range of y=$x^2$ is $[0\rightarrow...
  6. O

    Reciprocal functions - intersecting points

    Hi, I hope someone can help. I had to graph the reciprocal of the function f(x) = x^2-3x+2. The solution is as follows: I'm trying to understand why the red function (in the image attached) is so low in the centre. I'm referring to the point around (-1.5, -4). When I tried to find these...
  7. J

    4th Degree Polynomial

    How to factor this function? y = x^4 + x^2 + 2
  8. O

    Trying to understand sigma functions

    Hi math forum folks! I'm trying to understand sigma functions in the context of a homework question that I have. I attached an image of the question in this post. The issue that I'm facing with 12c is that I got the wrong answer. To my understanding f(12) does not equal f(3) x f(4) - which is...
  9. J

    Inverse Trigonometric Function

    if tan x = 1/cot x tan^-1(x) = ?
  10. J

    Find the Derivative

    I have two questions. They are almost similar. I wanna know if their derivative will be same or different. (a) If y = u^5 - 8u^2 + 2u - 1, and u = (x + 10)^(1/2), find dy/dx when x = -9. (b) If y = u^5 - 8u^2 + 2u - 1, and u = (x + 10)^(1/2), find dy/dx.
  11. J

    Domain of a Function

    How to find the domain of the function. 3/(1 +(4/x^2))^(1/2) when I set the denominator equal to zero, I get stuck 1 + (4/x^2) = 0 x^2 + 4 = 0 x^2 = -4 now cannot take the root of negative
  12. J

    Continuous Function

    (cos x)/(x - (pi/2)) I don't Understand why this function is continuous because when I plug pi/2 in x, it causes problems.
  13. J

    Piece-wise Defined Function - Constant k

    Find the value of the constant k if the function is continuous on the real line. f(x) = 2x^2 - 2x if x not equal 3 f(x) = kx^2 if x = 3 Is it correct to do this? kx^2 = 2x^2 - 2x 9k = 18 - 6 k = 4/3
  14. J

    Piece-wise Defined Function (3)

    Let f be a function defined on R by: f(x) = [(2x - 3)^2]^1/2 / (2x - 3) if x not equal 3/2 f(x) = -1 if x = 3/2 Is f continuous at 3/2? Justify.
  15. J

    Vertical Asymptotes

    f(x) = 4 / (x^2 - 2)^(1/2) Is zero a vertical Asymptote in this function?
  16. J

    Piecewise-defined Function

    Determine where f is continuous. f(x) = (sin x)/x if x not = 0 f(x) = 1 if x = 0 Is it correct to say f is continuous everywhere?
  17. J

    Limit of a Piecewise-defined Function

    This is a piecewise-defined function. f(x) = -1 if x < 0 f(x) = 0 if x = 0 f(x) = -1 if x > 0 Identify each limit. (a) lim f(x) as x goes to 0 from left (b) lim f(x) as x goes to 0 from right (c) lim f(x) as x goes to 0 It is clear that the limit of (a) and (b) is -1, but I am...
  18. J

    Limit Involves Sine as x goes to Infinite

    Find the limit of the following functions as x goes to Infinity. (a) f(x) = sin[ (x^2 + 4) / (x^2 - 4) ] (b) f(x) = (4 sin x)/x
  19. B

    difficult function question

    question: by eliminating x and y from these equations \frac{1}{x}+\frac{1}{y}= 1, x +y = a , \frac{y}{x} = m where a\neq 0 , obtain a relation between m and a. Given that a is real, determine the ranges of values of a for which m is real. Please help i am having difficulties...
  20. B

    Clarification to improve my understanding

    I was given this question to do; Find the ranges of values of k for which the equation x^2 +(k-3)x +k = 0 has roots of the same sign I have been able to do it with help. I was advised to use b > \sqrt{b^2 - 4ac} > 0 and b < - \sqrt{b^2 - 4ac} < 0 to solve it. Also, i was told...