If `f_1(x) and f_2(x)` are defined on domains `D_1 and D_2`,respectively, then `f_1 (x) + f_2(x)` is defined on `D_1 nn D_2`.

If f_(1) ,(x) and f_(2)(x) are defined on a domain D_(1) , and D_(2) , respectively, then domain of f_(1)(x) + f_(2) (x) is :

Assertion (A) : If f : R to R defined by f(x) =sin^(-1)(x/2) + log_(10)^(x) , then the domain of the function is (0,2]. Reason (R) : If D_(1) and D_2 are domains of f_(1) and f_2 , then the domain of f_(1) + f_(2) is D_(1) cap D_(2)

If f(x) is defined on [0,1], then the domain of f(3x^(2)) , is

If f(x) is defined on [0,1], then the domain of f(3x^(2)) , is

For questions 13-14: The accompanying figure shows the graph of a function f(Cr) with domain [O, 2] and range [0, 1] 2 Figure I Figure II Q13) Figure II represents the graph of A. 2f(x) B. f(r-2) C. f(x + 2) D. f (x -2)+ 1 Q14) The domain and range respectively of A. f(-x) are [- 2, 0] and -1,0] B. f(x)-1 are [0, 2] and [0, 1] C. f(x) + 2 are [0, 2] and [1, 2] D. -ft+1)+ 1 are [-1, 1] and [0, 1] x +1+ 1 are

The function f(x) is defined in 0 le x le1, find the domain of definition of f(2x-1)

A function f(x)=sqrt(1-2x)+x is defined from D_(1rarr)D_(2) and is onto lf the set D_(1) is its complete domain then the set D_(2) is

Let f:[-1,1]rarr[-(pi)/(2),(pi)/(2)] is defined as f(x)=sin^(-1)x and g:R rarr[-1,1] is defined as g(x)=sin x. if D_(1) denotes the domain of f(x), then which of the following is correct?

If f(x)=(x^(2)-x)/(x^(2)+2x) , then find the domain and range of f. Show that f is one-one. Also, find the function (d(f^(-1)(x)))/(dx) and its domain.