Functional Equations

JEE Main Mathematics · Relations and Functions · 22 questions, latest first

• Let f be a polynomial function such that log_2(f(x))=( log_2(2+2/3+2/9+… … ∞)) · log_3(1+(f(x))/(f(1 / x))), x>0 and f(6)=37.…20268 April, Shift 2 · Q25
• Let for some α ∈ R, f: R → R be a function satisfying f(x+y)=f(x)+2 y^2+y+α x y for all x, y ∈ R. If f(0)=-1 and f(1)=2, then the…20264 April, Shift 2 · Q16
• Let f be a function such that 3 f(x)+2 f(m/(19 x))=5 x, x ≠ 0, where m=Σ_i=1^9(i)^2. Then f(5)-f(2) is equal to202624 January, Shift 2 · Q2
• Let f and g be functions satisfying f(x+y)=f(x) f(y), f(1)=7 and g(x+y)=g(x y), g(1)=1, for all x, y ∈ N. If…202622 January, Shift 2 · Q2
• Let f(x)+2 f(1/x)=x^2+5 and 2 g(x)-3 g(1/2)=x, x>0. If α=∫_1^2 f(x) d x, and β=∫_1^2 g(x) d x, then the value of 9 α+β is:20254 April, Shift 2 · Q18
• Let f: R → R be a continuous function satisfying f(0)=1 and f(2 x)-f(x)=x for all x ∈ R. If lim_n → ∞{f(x)-f(x/2^n)}=G(x), then…20254 April, Shift 1 · Q18
• Let f be a function such that f(x)+3 f(24/x)=4 x, x ≠ 0. Then f(3)+f(8) is equal to20253 April, Shift 2 · Q3
• Let f: R → R be a twice differentiable function such that ( sin x cos y)(f(2 x+2 y)-f(2 x-2 y))=( cos x sin y)(f(2 x+2 y)+f(2 x-2…20252 April, Shift 1 · Q14
• Let f: R-{0} →(-∞, 1) be a polynomial of degree 2, satisfying f(x) f(1/x)=f(x)+f(1/x). If f( K)=-2 K, then the sum of squares of…202528 January, Shift 2 · Q3
• If f(x)=2^x/(2^x+√2), x ∈ R, then Σ_k=1^81 f(k/82) is equal to202528 January, Shift 1 · Q2
• Let f: R → R be a function defined by f(x)=(2+3 a) x^2+((a+2)/(a-1)) x+b, a ≠ 1. If; f(x+y)=f(x)+f(y)+1-2/7 x y, then the value…202528 January, Shift 1 · Q19
• Let f(x)=(2^x+2+16)/(2^2 x+1+2^x+4+32). Then the value of 8(f(1/15)+f(2/15)+…+f(59/15)) is equal to202524 January, Shift 1 · Q1
• Let f: R-{0} → R be a function such that f(x)-6 f(1/x)=35/(3 x)-5/2. If the lim_x → 0(1/(α x)+f(x))=β; α, β ∈ R, then α+2 β is…202524 January, Shift 1 · Q16
• If a function f satisfies f( m+n)=f( m)+f(n) for all m, n ∈ N and f(1)=1, then the largest natural number λ such that Σ_k=1^2022…20249 April, Shift 1 · Q26
• For the differentiable function f: R-{0} → R, let 3 f(x)+2 f(1/x)=1/x-10, then |f(3)+f^′(1/4)| is equal to202313 April, Shift 1 · Q1
• Let 5 f(x)+4 f(1/x)=1/x+3, x>0. Then 18 ∫_1^2 f(x) d x is equal to:20236 April, Shift 1 · Q10
• Let f: R-{0,1} → R be a function such that f(x)+f(1/(1-x))=1+x. Then f(2) is equal to20231 February, Shift 2 · Q66
• Suppose f: R →(0, ∞) be a differentiable function such that 5 f(x+y)=f(x) · f(y), ∀ x, y ∈ R. If f(3)=320, then Σ_n=0^5 f(n) is…202330 January, Shift 1 · Q67
• Consider a function f: N → R, satisfying f(1)+2 f(2)+3 f(3)+…+x f(x)=x(x+1) f(x); x ≥ 2 with f(1)=1. Then 1/(f(2022))+1/(f(2028))…202329 January, Shift 2 · Q63
• Suppose f is a function satisfying f(x+y)=f(x)+f(y) for all x, y ∈ N and f(1)=1/5. If Σ_n=1^m (f(n))/(n(n+1)(n+2))=1/12, then m…202329 January, Shift 1 · Q83
• If f(x)=(2^2 x)/(2^2 x+2), x ∈ R, then f(1/2023)+f(2/2023)+…+f(2022/2023) is equal to202324 January, Shift 2 · Q61
• Let f(x) be a function such that f(x+y)=f(x) · f(y) for all x, y ∈ N. If f(1)=3 and Σ_k=1^n f(k)=3279, then the value of n is202324 January, Shift 2 · Q69