Composition & Inverse Functions: JEE Questions & Solutions

If the domain of the function f(x)=sin⁻¹ ((5-x)/(3+2x))+1/logₑ(10-x) is (-∞,α]∪[β,γ)-{δ}, then 6(α+β+γ+δ) is equal to

If g(x) = 3x² + 2x - 3, f(0) = -3 and 4g(f(x)) = 3x² - 32x + 72, then f(g(2)) is equal to:

Let f(x) = log x and g(x) = (x⁴ - 2x³ + 3x² - 2x + 2)/(2x² - 2x + 1). Then the domain of f ° g is:

Let f, g: (1, ∞) → ℝ be defined as f(x) = (2x + 3)/(5x + 2) and g(x) = (2 - 3x)/(1 - x). If the range of the function fog: [2, 4] → ℝ is…

Let f: ℝ - {-1/2} → ℝ and g: ℝ - {-5/2} → ℝ be defined as f(x) = (2x + 3)/(2x + 1) and g(x) = (|x| + 1)/(2x + 5). What is the domain of f °…

If f(x) = (4x + 3)/(6x - 4), with x ≠ 2/3, and (f ° f)(x) = g(x), where g: R - {2/3} → R - {2/3}, then (g ° g ° g)(4) is equal to:

For some a, b, c ∈ ℕ, let f(x) = ax - 3 and g(x) = x^b + c, x ∈ ℝ. If (f ° g)⁻¹(x) = ((x - 7)/2)^(1/3), then (f ° g)(ac) + (g ° f)(b) is…

Let f¹(x) = (3x + 2)/(2x + 3), x ∈ ℝ, R - ( -3/2). For n ≥ 2, define fⁿ(x) = f¹ ° fⁿ⁻¹(x) and if f⁵(x) = (ax + b)/(bx + a), gcd(a, b) = 1,…

Let for x ∈ ℝ f(x) = (x + |x|)/2 for x ≥ 0 and f(x) = x/2 for x < 0 g(x) = x² for x ≥ 0, x for x < 0 Then the area bounded by the curve y =…

Let f and g be two functions defined by: f(x) = x + 1, x < 0 |x - 1|, x ≥ 0, g(x) = x + 1, x < 0 1, x ≥ 0. Then (g ° f)(x) is:

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 to: