Let f, g and h be functions from R to R. Show that
(i) `(f +g ) oh = `foh + goh`
(ii) `(f. g) oh = ( foh`). (goh) `

Let f(x) = x^(2) , g (x) = 2x + 1 be two functions. Then find (i) (f + g) (x) (ii) (f - g) (x) (iii) (fg) (x)

Let f={(x, x^2/(1+x^(2))), x in R} be a function from R into R. Determine the range of f.

Let f : R to R be defined as f (x) =10 x +7. Find the function g : R to R such that g o f =f o g= I _(R).

Let f(x) = sqrt(x) and g(x) = x find (i) (f + g) x (ii) (fg) x

Let f, g : R rarrR be two functions defined as f(x) = |x| + x and g(x) = | x| - x AA x in R. . Then (fog ) (x) for x lt 0 is

Let f : R rarr R be a function defined by f(x) = x^3 + 5 . Then f^-1(x) is

Let f and g be differentiable functions such that ("fog")'=I . If g'(a)=2 and g(a)=b , then f'(b) equals :

If the functions f and g defined from the set of real number R to R such that f(x) = e^(x) and g(x) = 3x - 2, then find functions fog and gof.