How do I find the inverse function of x^2-6x=f(x)?
There is no inverse function for x^2 - 6x = f(x), because the inverse of a square is not a function. It involves a positive or negative square root, which means there will be two possible values of f'(x) for each value of x, which violates the definition of a function and therefore f'(x) cannot be a function.
What is the inverse of function f(x) = 6x?
assume y=f(x)=6xf(y)=y/6so the inverse of function f(x)=6x is f(x)=x/6
What is the inverse function for [math]f(x)=e^x[/math] ?
Every exponential function has an inverse. The inverses of exponential functions are called logarithmic functions (logarithms or logs for short). b is called the base of the logarithm.graph of function and it’s inverse function are symmetric (i,e mirror image ) to y=x line.so,we can say that y=ln x is inverse function of y=e^x.
Find the inverse y=[1+(e^x)]/[1-(e^x)]?
To find the inverse, we let f(x) = y (although this isn't needed here), interchange x and y, and then re-solve for y. The resulting expression in y will be the inverse of the original function. Interchanging x and y gives: x = (1 + e^y)/(1 - e^y). Re-solving for y: x = (1 + e^y)/(1 - e^y) ==> x(1 - e^y) = 1 + e^y ==> x - x*e^y = 1 + e^y ==> x - 1 = x*e^y + e^y ==> e^y * (x + 1) = x - 1 ==> e^y = (x - 1)/(x + 1) ==> y = f^-1(x) = ln[(x - 1)/(x + 1)]. I hope this helps!
The function f is given by f(x)= e^(x-11) -8 1) find f^-1(x) 2) write down the domain of f^-1(x)?
1) By f^-1(x) means that they are looking for the inverse of the function. To do this put x and y into the equation. y = e^(x - 11) - 8 Now exchange the places of the x and y variables and solve for y. x = e^(y - 11) -8 (x + 8) = e^(y - 11) ln(x + 8) = y - 11 y = ln (x + 8) + 11 So the inverse to f(x) is f(x)^-1(x) = ln (x + 8) + 11 2) To find the domain of f^-1(x) is what variables of x can you put into the equation. Since you can not ln anything equal to or below 0, then x must be larger than -8. So the domain is: x>-8
Hard Inverse Function Question (10 points)?
For simplicity's sake, lets replace f(x) with y to make this a little less messy. y = (3 * e^x - 5) / (8 * e^x + 6) Basically the idea for finding inverse functions works like this: you replace every x in the equation with a y, and replace every y in the equation with an x. Then you solve for y in terms of x. In the problem you've asked, we would have x = (3 * e^y - 5) / (8 * e^y + 6) (8 * e^y + 6) * x = 3 * e^y - 5 8x * e^y + 6x = 3 * e^y - 5 8x * e^y - 3 * e^y = -6x - 5 e^y * (8x - 3) = -6x - 5 e^y = (-6x - 5) / (8x - 3) y = ln[(-6x - 5) / (8x - 3)] Thus the inverse function is f(x) = ln[(-6x - 5) / (8x - 3)] To find the domain, notice that you can only take the natural log of a positive number. Thus we must have (-6x - 5) / (8x - 3) > 0 This means we either have (-6x - 5) > 0 and (8x - 3) > 0 or we have (-6x - 5) < 0 and (8x - 3) < 0 For the first case, we can simplify the inequalities down to x < -5/6 and x > 3/8 (which is impossible) For the second case, we can simplify those inequalities down to x > -5/6 and x < 3/8 which says, in interval notation, that x is on the interval (-5/6 , 3/8) Thus the domain of the function is (-5/6 , 3/8) , and so a = -5/6 and b = 3/8
How do you find the inverse of this? 6x-y=7?
6x-y=7 1. Get the Y alone, so subtract 6x and divide by the negative. 1) -y=7-6x // y=6x-7 2. Then you switch the x and y places. 2) y=6x-7 // x=6y-7 3. Last to get the inverse you solve for y again, so add 7 and divide by 6. 3) x+7=6y // 1/6x+7/6=y or f-1(x)= (x+7)/6 which is C