PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

Let C denote the set of all complex numbers. A function f : C → C is defined by f(x) = x³. Write f⁻¹(1).

Let f  be a function from C (set of all complex numbers) to itself given by f(x) = x³. Write f⁻¹ (−1).

If f : C → C is defined by f(x) = x⁴, write f⁻¹ (1).

If f : R → R is defined by f(x) = x², find f⁻¹ (−25).

If f : C → C is defined by f(x) = (x − 2)³, write f⁻¹ (−1).

If f : R → R is defined by f(x) = 10 x − 7, then write f⁻¹ (x).

Let \[f : \left( - \frac{\pi}{2}, \frac{\pi}{2} \right) \to R\]  be a function defined by f(x) = cos [x]. Write range (f).

If f : R → R defined by f(x) = 3x − 4 is invertible, then write f⁻¹ (x).

If f : R → R, g : R → are given by f(x) = (x + 1)² and g(x) = x² + 1, then write the value of fog (−3).

Let A = {x ∈ R : −4 ≤ x ≤ 4 and x ≠ 0} and f : A → R be defined by \[f\left( x \right) = \frac{\left| x \right|}{x}\]Write the range of f.

Let \[f : \left[ - \frac{\pi}{2}, \frac{\pi}{2} \right] \to\] A be defined by f(x) = sin x. If f is a bijection, write set A.

Let f : R − {−1} → R − {1} be given by\[f\left( x \right) = \frac{x}{x + 1} . \text{Write } f^{- 1} \left( x \right)\]

Let `f : R - {- 3/5}` → R be a function defined as `f  (x) = (2x)/(5x +3).` 

f^-1 : Range of f → `R -{-3/5}`.

Let f : R → R, g : R → R be two functions defined by f(x) = x² + x + 1 and g(x) = 1 − x². Write fog (−2).

Let f : R → R be defined as  `f (x) = (2x - 3)/4.` write fo f^-1 (1) .

Let f be an invertible real function. Write ( f^-1  of ) (1) + ( f^-1  of ) (2) +..... +( f^-1 of ) (100 )

Let A = {1, 2, 3, 4} and B = {a, b} be two sets. Write the total number of onto functions from A to B.

Write the domain of the real function

`f (x) = sqrtx - [x] .`