g o f =? f(x)=(x-1)^2 and g(x)=x^1/2

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ncchemist | eNotes Employee

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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

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tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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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`

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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|

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