If y = f(x) = (ax – b)/(bx – a), show that x = f(y). Watch Solution
If f(x) = 1/(1 – x), show that f[f{f(x)}] = x. Watch Solution
if f(x) = (x + 1)/(x – 1), show that f[f(x)] = x Watch Solution
If f(x) = {x^2, when x less than 0 ; x, when 0 ≤ less than 1 ; 1/x, when x greater 1, Find: (i) f(1/2) (ii) f(-2) (iii) f(1) (iv) f(√3) and (v) f(√-3). Watch Solution
If f(x) = x^3 – 1/x^3, show that f(x) + f(1/x) = 0 Watch Solution
If f(x) = 2x/(1 + x^2) show that f(tan θ) = sin 2θ Watch Solution
If f(x) = (a – x^n)^1/n, a greater than 0 and n ∈ N, then prove that f(f(x)) = x for all x. Watch Solution
If f(x) = (x – 1)/(x + 1), then show that (i) f(1/x) = -f(x) (ii) f(-1/x) = -1/f(x) Watch Solution
If for non-zero x, af(x) + bf(1/x) = 1/x – 5, where a ≠ b then find f(x). Watch Solution
Chapter 3: Functions – R. D. Sharma Class 11th Maths