Let f(x) and g(x) be two functions such that g(x)=x- 1 x and f o g(x)=x^3- 1 x^3 . What is g[f(x)-3 x] equal to?

Step-by-step solution

f(x) and g(x) are two functions aligned g(x) & =x- 1 x and f o g(x)=x^3- 1 x^3 f (x- 1 x ) & =x^3- 1 x^3 f (x- 1 x ) & = (x- 1 x )^3+3 (x- 1 x ) aligned f(x)=x^3+3 x ....(i) aligned g[f(x)-3 x] & =f(x)-3 x- 1 f(x)-3 x g(f(x)-3 x] & =x^3+3 x-3 x- 1 x^3+3 x-3 x & =x^3- 1 x^3 g(f(x)-3 x] & =x^3- 1 x^3 aligned