Find the inverse function of? f(x) = x + 1/ 2x + 1?
I assume that is: y = (x + 1) / (2x + 1) Reverse the letters for x and y: x = (y + 1) / (2y + 1) Multiply both sides by 2y + 1: x(2y + 1) = y + 1 2xy + x = y + 1 Subtract y from both sides: 2xy - y + x = 1 Subtract x from both sides: 2xy - y = 1 - x Now factor out y: y(2x - 1) = 1 - x Divide both sides by 2x - 1: y = (1 - x) / (2x - 1)
HELP ME! Given the function f(x) = 2(x + 10), find x if f(x) = 24?
f(x)=24 24=2(x+10) 24=2x + 20 4 = 2x x = 2 That was easy now, wasn't it.
Find a formula for the inverse of the function. f(x)= 2x^2-8x, x is greater then or equal to 2?
f(x) = 2x^2 - 8x y = 2x^2 - 8x Switch x's and y's and solve for y: x = 2y^2 - 8y Divide both sides by 2: x/2 = y^2 - 4y Complete the square: x/2 = y^2 - 4y + 4 - 4 x/2 = (y + 2)^2 - 4 Add 4 to both sides: x/2 + 4 = (y + 2)^2 Square root of both sides: ±sqrt(x/2 + 4) = y + 2 Subtract 2 from both sides: y = -2 ± sqrt(x/2 + 4) So f^-1(x) = -2 ± sqrt(x/2 + 4)
Calculus 3: Find a function f such that F = ∇f for F(x,y) = (2x - 3y)i + (-3x + 4y - 8)j?
I need help understanding the steps on how to solve this :-( I already know that F is conservative, so I can find the function f. I know the first step: fx(x,y) = 2x - 3y fy(x,y) = -3x + 4y - 8 So the second step would be to integrate fx(x,y) with respect to x, which'd give me: f(x,y) = (x^2) - 3xy + g(y) I'm confused where to go now =/ If you could also explain the step, I'd appreciate it :-)
Even and odd functions?
I need help on finding if function is even odd or neither. I know even is f(-x)=fx and odd is f(-x)=-fx but I am struggling with one with x to the negative power. pleas tell me the answer and possibly how to solve those problems as well. f(x)=x^-6 f(x)=x^4+3x^-4+2x^-1 f(x)=x^4-6^-4+3x^2 f(x)=-5x^4-3x^-4-2
To find the inverse of a function you interchange the constant and the f(x) value and solve for f(x).?
False; you change f(x) with x, not the constant.
Is it possible to find the function f(x) given that f(1)=0, f(2)=3, f(3)=12, f(4)=39, f(5)=120, and f(6)=363?
Others have described methods that can be employed to find _a_ function f(x) that meets the stated criteria. However, you asked if it is possible to find _the_ function f(x), which can be read to imply that you are asking for a unique function. The answer to that is NO, as there are infinitely many functions f(x) that can meet the criteria. For example, if you add the criteria f(7)=v, for all values of v, there are functions that can be found, using the solutions shown by others: interpolating polynomials, or finding the coefficients of a polynomial with a sufficient number of terms. Therefore, there are infinitely many functions f(x), not a single function that can be found.
Which function is the inverse of: f(x) = ½x + 3?
the inverse of a function is defined by f(f^-1(x)) = x Having mathematical experience, i guess it's C, now lets check f(2x-6) = 1/2(2x - 6) + 3 = (x-3) + 3 = x it's correct :^)
How do I find maximum and minimum value of a function?
There are Various methods in order to find maximum or minimum value of a function. One of the conventional methods is:Find the derivative of the function and equate it to zero.Find the roots of the differentiated equation.Do double differentiation of original function and substitute the values of roots in the 2nd differentiated expression.If the value comes out to be negative, At the particular value of the root Maximum occurs. Then substitute the value in original expression to get Maximum of the function.If the value of double derivative after substituting the root is positive, Minimum occurs. Then substitute the value in original equation to get Minimum value of the function.If the Second derivative is Zero: Then go for higher derivatives of the function & substitute the value of the root in the nth order derivative expression. If it's positive it would give the Maximum of the function at the particular root.Hope the answer Helps.
What is the solution for finding the tangent line at x=16 for the function (fx)= (x^1/2)(log(x-5))?
What you have posted is an expression, not a function. Also, the formatting is unclear. But I think you mean the following:Find the equation of the line tangent to [math]f(x)\, =\, x^{1/2}\, \log(x\, -\, 5)[/math] at x = 16.The process is first to find the point on the function. So plug the given value in for the variable, and simplify to find the corresponding y-value. This is the point through which the tangent line will pass.Then differentiate the given function, and evaluate the derivative at the given x-value. This is the slope of the tangent line through the above point.Then plug the slope and the point into, say, the point-slope formula from back in algebra:[math]y\, -\, y_1\, =\, m\, (x\, -\, x_1)[/math]…and rearrange to get the tangent equation into whichever format your instructor or textbook prefers.