MHT CET202310 May 2023Morning ShiftMathematicsFunctionsActual
If f (x)= e ^x, ~g (x)= ⁻¹ x and h (x)= f ( g (x)) , then h ^ (x) h (x) is
Options
- Ae ^ ⁻¹ x
- B1 1-x^2
- C⁻¹ x
- De ^ ⁻¹ x 1-x^2
Correct answer
B. 1 1-x^2
Step-by-step solution
aligned h (x) & = f ( g (x)) & = f ( ⁻¹ x ) h (x) & = e ^ ⁻¹ x aligned Differentiating w.r.t. x , we get aligned & aligned h ^ (x) & = e ^ ⁻¹ x d d x ( ⁻¹ x ) & = e ^ ⁻¹ x 1 1-x^2 aligned & Now, h ^ (x) h (x) = e ^ ⁻¹ x 1 1-x^2 e ^ ⁻¹ x = 1 1-x^2 aligned