​ 1. If f: R – {2} → R – {2}, defined by f(x) =(2x-3)/(x-2) then find fof 2. Which of the following satisfies the condition f^-1 ≠ f. ​

Question

1. If f: R – {2} → R – {2}, defined by f(x) = \(\frac{2x-3}{x-2}\) then find fof

2. Which of the following satisfies the condition f^-1 ≠ f.

(a) f : R – {0} → R – {0}, f(x) = \(\frac{1}{x}\)

(b) f :R → R, f(x) = -x

(c) f : R – {-1} → R – {-1}, f(x) = \(\frac{x}{x+1}\)

(d) f: R – {2} → R – {2}, f(x) = \(\frac{2x-3}{x-2}\)

Answer 1

1. fof(x) = f(f(x)) = f(\(\frac{2x-3}{x-2}\))

2. Following satisfies the condition f^-1 ≠ f:

(a) f : R – {0} → R – {0}, f(x) = \(\frac{1}{x}\)

(b) f :R → R, f(x) = -x

The graph of functions in (a) and (b) symmetric with respect to the line y = x. 

The function in (d) we have already shown that fof (x) = x. So the answer is (c)

f : R – {-1} → R – {-1}, f(x) = \(\frac{x}{x+1}\)