The function f(x) satisfies f(sqrt(x+1))=1/x for all x>= -1, x does not = 0. Find f(2)Thank you!
we want f(2), so that means we need
√(x+1) = 2
so, x=3
f(2) = 1/3
To find f(2) using the given information, we need to find the value of x that satisfies the equation f(sqrt(x+1)) = 1/x and substitute it into the function.
Let's start by solving the equation f(sqrt(x+1)) = 1/x for x = 2.
Substitute x = 2 into the equation to get:
f(sqrt(2+1)) = 1/2
Simplifying the square root:
f(sqrt(3)) = 1/2
Now, to find the value of f(2), we need to find the value of x that satisfies sqrt(x+1) = sqrt(3).
Squaring both sides of the equation, we get:
x + 1 = 3
Simplifying further, we find:
x = 2
So, the value of x that satisfies sqrt(x+1) = sqrt(3) is x = 2.
Now substitute this value into the original equation:
f(sqrt(2+1)) = 1/2
f(sqrt(3)) = 1/2
Therefore, f(2) = 1/2.
In summary, f(2) is equal to 1/2 according to the given function and equation.