The function f (x) is defined by f (x) = (1-x)/(1+x), x not equal to -1. Show that f(f (x)) = x. Hence write down f ^-1 (x).
f(f (x) )= f( (1-x)/(1+x) ) = (1-(1-x)/(1+x))/(1+(1-x)/(1+x))where you replace x by (1-x)/(1+x). Multiply the top and bottom of the fraction by (1+x) to get ((1+x)-(1-x))/((1+x)+(1-x)) which simplifies to 2x/2 = x. Hence you have shown f(f (x)) = x. f^−1 (x) = f(x) = (1−x)/(1+x), this is because f^−1(f(x)) = f( f^−1(x))= x.
SP
Related Maths A Level answers
All answers ▸find the derivative of f(x) = x^3 + 2x^2 - 5x - 6. Find all stationary points of the function.
How do I find the distance between two point in the plane?
What is the general rule for differentiation?
Integrate (x)(e^x) with respect to x and then integrate (x)(e^x) with respect to y.