symbolipoint said:You must improve your notation. You seem to mean, f(x) = (x +1)/y from which you may like to
find an inverse such as x = (y + 1)/x and the rest is simple algebraic steps.
symbolipoint said:If that is what your book said, then the exchange will be from y = x + 1/x
to x = y + 1/y
I made a variable writing error in my first response.
symbolipoint said:... just to continue, your next step would be to multiply both sides by 'y'.
Larrytsai said:k this is what i got so far x(y)= y-1
should i move the y to the other side or the '-1'?
Larrytsai said:k this is a function and i have to find the inversed
f(x)= x+1 / x
attempt: x= y + 1 / y
multiply both sides by 'y'
x(y)= y + 1
First factor out "y": y(x- 1)= 1 and then divide by x-1.subtract both sides by y
x(y) -y=1
divide 'x'
However, if, as you appear to be saying, the problem really is y= x+ 1/x, becoming x= y+ 1/y, then multiplying both sides by y gives you xy= y2+ 1. That you would write as the quadratic equation y2- xy+ 1= 0 and solve using the quadratic formula with a= 1, b= -x, c=1. Notice that you will have a "[itex]\pm[/itex]" which means that the original function was not "one to one" and so does not have a true inverse.im lost from here help please:D
An inverse function is a function that undoes the action of another function. It can be thought of as the "reverse" of the original function, and when applied to the result of the original function, it returns the original input value.
To solve for the inverse function of a given function, switch the x and y variables, and then solve for y. This will give you the inverse function in terms of x. For example, to find the inverse function of f(x) = x+1/x, you would write it as y = x+1/x and then solve for x, resulting in the inverse function g(x) = (x+1)/(y-1).
The domain and range of an inverse function are switched from the original function. This means that the domain of the inverse function is the range of the original function, and vice versa. In the case of f(x) = x+1/x, the domain is all real numbers except for 0, and the range is also all real numbers except for 0.
One way to check if a function and its inverse are correct is to use the composition of functions method. This involves plugging the original function into the inverse function and vice versa, and if the resulting functions are equal, then the inverse is correct. In the case of f(x) = x+1/x and its inverse g(x) = (x+1)/(y-1), the composition of functions would be f(g(x)) = (x+1)/(x+1) and g(f(x)) = (x+1)/((x+1)/x), both resulting in x, indicating that the inverse is correct.
Finding the inverse of a function is important because it allows us to "undo" the effects of a function and solve for the original input value. This is useful in many real-world applications, such as finding the original price of a discounted item or calculating the initial speed of an object given its acceleration and time. Inverse functions also have many mathematical applications, such as in solving equations and understanding the behavior of functions.