For a differentiable function f : R → R , suppose f ′ ( x ) = 3 f ( x ) + α , where α ∈ R , f ( 0 ) = 1 and lim x → − ∞ f ( x ) = 7 . Then 9 f ( − lo g e 3 ) is equal to_________

Question

For a differentiable function f : R → R , suppose f ′ ( x ) = 3 f ( x ) + α , where α ∈ R , f ( 0 ) = 1 and lim x → − ∞ ​ f ( x ) = 7 . Then 9 f ( − lo g e ​ 3 ) is equal to_________

TestHub · Accepted Answer

​ d x d y ​ − 3 y = α If = e ∫ − 3 d x = e − 3 x ∴ y − e − 3 x = ∫ e − 3 x ⋅ α d x y e − 3 x = − 3 α e − 3 x ​ + c ( ∗ e 3 x ) y = − 3 α ​ + C ⋅ e 3 x ​ on substituting x = 0 , y = 1 x → − ∞ , y = 7 we get y = 7 − 6 e 3 x 9 f ( − lo g e ​ 3 ) = 61

Mathematics - Functions Question with Solution | TestHub

Doubts & Discussion