Let `f(x)=sqrtx and g(x)=x` be two functions defined over the set of non-negative real numbers. Find `(f+g) (x), (f-g), (fg) (x) and (f/g) (x)`.

Let f(x)=x^(2) and g(x)=2x+1 be two real functions. Find (f+g) (x), (f-g) (x), (fg) (x), (f/g) (x) .

Two functions f and g are defined on the set of real numbers RR by , f(x)= cos x and g(x) =x^(2) , then, (f o g)(x)=

Let f(x)=2x-sinx and g(x) = 3sqrtx . Then

Let f(x)=sin x+cosx and g(x)=x^(2)-1 , then g{f(x)} is invertible if -

If f(x) and g(x) be two given function with all real numbers as their domain, then h(x)={f(x)+f(-x)}{g(x)-g(-x)} is

Let f(x) = x + cos x + 2 and g(x) be the inverse function of f(x), then g'(3) equals _

Let the functions f and g on the set of real numbers RR be defined by, f(x)= cos x and g(x) =x^(3) . Prove that, (f o g) ne (g o f).

If RR is the set of real numbers and f(x)=|x|,g(x)=x , find the product function fg.

If f(x)=e^x and g(x) =log_(e)x, then find (f+g)(1) and fg(1).

Let f(x)a n dg(x) be two function having finite nonzero third-order derivatives f'''(x) and g'''(x) for all x in R . If f(x).g(x)=1 for all x in R , then prove that (f''')/(f') - (g''')/(g') = 3((f'')/f - (g'')/g) .