सिद्ध कीजिये कि फलन `f(x)=loga^x` अन्तराल ] `0,oo` [ में निरन्तर वर्धमान तथा अन्तराल ] `0,oo` [ में निरन्तर ह्रासमान फलन है यहाँ `agt11`

Show that f(x) = log_a x "on" (0,oo ),(a gt 0 "and" a != 1) functions are injective.

1.Prove that the function f(x)=log_(a)x is increasing on (0,oo) if a>1 and decreasing on (0,oo), if '0

Prove that the function f(x)=(log)_(a)x is increasing on (0,oo) if a>1 and decreasing on (0,oo). if '0

Prove that the function f(x)=(log)_(a)x is increasing on (0,oo) if a>1 and decreasing on (0,oo), if 0

f(x) = x^2 increases on: (a) ( 0,oo) (b) (-oo,0) (c) (-7,-3) (d) (-oo,-3)

The range of the function f(x)=|x-1| is A. (-oo,0) B. [0,oo) C. (0,oo) D. R

The range of the function f(x)=|x-1| is A. (-oo,0) B. [0,oo) C. (0,oo) D. R

Let f(x) lt 0 AA x in (-oo, 0) and f (x) gt 0 ,AA x in (0,oo) also f (0)=0, Again f'(x) lt 0 ,AA x in (-oo, -1) and f '(x) gt 0, AA x in (-1,oo) also f '(-1)=0 given lim _(x to -oo) f (x)=0 and lim _(x to oo) f (x)=oo and function is twice differentiable. If f'(x) lt 0 AA x in (0,oo)and f'(0)=1 then number of solutions of equation f (x)=x ^(2) is : (a) 1 (b) 2 (c) 3 (d) 4