NDA2016MathematicsFunctionsActual
If f ( x ₁ )- f ( x ₂ )= f ( x ₁- x ₂ 1- x ₁ x ₂ ) for x ₁, x ₂ (-1,1) , then what is f ( x ) equal to?
Options
- A( 1-x 1+x )
- B( 2+x 1-x )
- C⁻¹ ( 1-x 1+x )
- D⁻¹ ( 1+x 1-x )
Correct answer
A. ( 1-x 1+x )
Step-by-step solution
aligned & f (x₁ )-f (x₂ )=f ( x₁-x₂ 1-x₁ x₂ ) & x₁, x₂ (-1,1) aligned then f(x)= (1-x) (1+x) gathered f (x₁ )= 1-x₁ 1+x₁ f (x₂ )= 1-x₂ 1+x₂ aligned f (x₁ )-f (x₂ ) & = 1-x₁ 1+x₁ - 1-x₂ 1+x₂ & = (1-x₁ ) (1+x₁ ) (1+x₂ ) (1-x₂ ) = & (1-x₁+x₂-x₁ x₂ ) (1+x₁-x₂-x₁ x₂ ) = & (1-x₁ x₂ )- (x₁-x₂ ) (1-x₁ x₂ )+ (x₁-x₂ ) aligned gathered = 1- ( x₁-x₂ 1-x₁ x₂ ) 1+ ( x₁-x₂ 1-x₁ x₂ ) f (x₁ )-f (x₂ )=f ( x₁-x₂ 1-x₁ x₂ )