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g o f =? f(x)=(x-1)^2 and g(x)=x^1/2

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demadcrazy | Student, Grade 10 | eNoter

Posted May 23, 2011 at 9:28 AM via web

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g o f =?

 f(x)=(x-1)^2 and g(x)=x^1/2

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ncchemist | eNotes Employee

Posted May 24, 2011 at 7:03 AM (Answer #2)

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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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giorgiana1976 | College Teacher | Valedictorian

Posted May 24, 2011 at 4:26 PM (Answer #3)

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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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tonys538 | TA , Undergraduate | Valedictorian

Posted October 31, 2014 at 7:17 PM (Answer #4)

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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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