Pre Calculus
posted by Josh .
Inverse functions
what is the inverse function of
f(x)=1/square root of x +1?
and f(x)=1x^2, x<0?

Pre Calculus 
Jai
f(x) = 1/sqrt(x+1)
we can rewrite this as
y = 1/sqrt(x+1)
to get the inverse function, we replace x by y, and y by x, and solve for y:
x = 1/sqrt(y+1)
sqrt(y+1) = 1/x
y + 1 = 1 / x^2
y = (1/(x^2))  1
f'(x) = (1/(x^2))  1
for #2, we do the same:
f(x) = 1  x^2
y = 1  x^2
x = 1  y^2
y^2 = 1  x
y = sqrt(1x)
f'(x) = sqrt(1x)
hope this helps~ :)
Respond to this Question
Similar Questions

math help1
Okay I am a little bit confused about one math question can you please Help me out? 
Calculus
F(x) = 1x and g(x) = 1/x These functions have the property that f = f^1(inverse) and g = g ^1. That is, the inverse of f is equal to itself and the inverse of g is also equal to itself. Take the composition of each function with … 
pre calculus
Find the inverse of the function below. Graph the function below and the inverse. Determine the domain, range and asymptotes of the function below and the inverse function. Please show all your work. f(x) = 2e^x + 5 Just looking at … 
Calculus (Derivatives of Inverse Functions)
Suppose f(x) = sin(pi cos(x)). On any interval where the inverse function y = f^1(x) exists, the derivative of f^1(x) with respect to x is: I've come as far as y = arccos ((arcsin(x))/pi), but I am not certain this is right. 
Algebra 2
Ok, so I'm trying to find the inverse of each function. We're learning about Inverse Functions and Relations. The problem is f(x)=sqr.root of x/6 The sqr root is confusing me. 
PreCalculus
Find the inverse function for the function f(x)=2^(x)+1/2^(x)1 You will need to use some properties of logarithmic functions to find the inverse of this particular function. 
Advanced Algebra
What is the inverse of each of the functions defined by the following equations, if the inverse exists. If the inverse does not exist for the largest possible domain, limit the domain so that the inverse will exist. In each case, give … 
Please HELP! Calculus (Implicit functions)
Find the inverse of the function y = (square root x) + 4x , then solve for its 1st order derivative. 
Math: Inverse Function (Plz help)
Find the Inverse function of f: f(x)=8+[square root of(8+x)] f^(1)(x)=_______, x>8 
PreCalculus
Define the inverse secant function by restricting the domain of the secant function to the intervals (0, pi/2) and (pi/2, pi), and sketch the inverse functionâ€™s graph.