Composite Functions

JEE Main Mathematics · Relations and Functions · 10 questions, latest first

• If g(x)=3 x^2+2 x-3, f(0)=-3 and 4 g(f(x))=3 x^2-32 x+72, then f(g(2)) is equal to:202628 January, Shift 1 · Q2
• Let f, g:(1, ∞) → R be defined as f(x)=(2 x+3)/(5 x+2) and g(x)=(2-3 x)/(1-x). If the range of the function f ° g:[2,4] → R is…20254 April, Shift 1 · Q2
• Let f(x)= log_e x and g(x)=(x^4-2 x^3+3 x^2-2 x+2)/(2 x^2-2 x+1). Then the domain of f ° g is202523 January, Shift 1 · Q1
• Consider the function f: R → R defined by f(x)=(2 x)/(√(1+9 x^2)). If the composition of f. (f ° f ° f ° ⋯ ° f)_10 times…20244 April, Shift 2 · Q21
• If f(x)=(4 x+3)/(6 x-4), x ≠ 2/3 and (f ° f)(x)=g(x), where g: R-{2/3} → R-{2/3}, then (gogog) (4) is equal to202431 January, Shift 1 · Q1
• If f(x)={ 2+2 x, -1 ≤ x<0; 1-x/3, 0 ≤ x ≤ 3; g(x)= {-x, -3 ≤ x ≤ 0; x, 0<x ≤ 1}., then range of (f ° g)(x) is202429 January, Shift 1 · Q1
• Let f: R-{-1/2} → R and g: R-{-5/2} → R be defined as f(x)=(2 x+3)/(2 x+1) and g(x)=(|x|+1)/(2 x+5). Then, the domain of the…202427 January, Shift 2 · Q1
• For x ∈ R, two real valued functions f(x) and g(x) are such that, g(x)=√x+1 and f ° g(x)=x+3-√x. Then f(0) is equal to202313 April, Shift 1 · Q19
• If f(x)=(( tan 1^°) x+ log_e(123))/(x log_e(1234)-( tan 1^°)), x>0, then the least value of f(f(x))+f(f(4/x)) is202310 April, Shift 1 · Q1
• Let f^1(x)=(3 x+2)/(2 x+3), x ∈ R-{-3/2} For n ≥ 2, define f^n(x)=f^1 ° f^n-1(x). If f^5(x)=(a x+b)/(b x+a), gcd(a, b)=1, then…202330 January, Shift 1 · Q84