g o f =? f(x)=(x-1)^2 and g(x)=x^1/2

Expert Answers
ncchemist eNotes educator| Certified Educator

Finding g(f(x)) is the same as subtituting the f(x) function into the variable for g(x) and simplifying.  In this case it involves taking the square root of the squared term, thereby cancelling the exponents:

g(f(x)) = [(x-1)^2]^1/2 = (x-1)^1 = x-1

g o f = x-1

tonys538 | Student

The  function` f(x)=(x-1)^2` and `g(x)=x^1/2`

`gof(x) = g(f(x))`

= `g((x - 1)^2)`

= `((x - 1)^2)^(1/2)`

= `(x - 1)^(2*1/2)`

= x - 1

The complex function `gof(x) = x - 1`

giorgiana1976 | Student

We'll write the composition of the functions g and f as it follows:

gof(x) = g(f(x))

f(x) = (x-1)^2 and g(x) = sqrt x

We'll replace x by f(x), in the expresison of g(x).

g(f(x)) = g((x-1)^2)

g((x-1)^2) = sqrt [(x-1)^2]

g((x-1)^2) = |x-1|

The result of composition of the functions is:

(gof)(x) = g(f(x)) = |x-1|