# function

1. ### 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.

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. ### 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. ### 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. ### 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. ### 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. ### 4th Degree Polynomial

How to factor this function? y = x^4 + x^2 + 2
8. ### 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. ### Inverse Trigonometric Function

if tan x = 1/cot x tan^-1(x) = ?
10. ### 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. ### 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. ### 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. ### 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. ### 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. ### Vertical Asymptotes

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