# If f(x)=(x-1)^2 and g(x)=x^1/2 then gof=?

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### 3 Answers

We are given that f(x)=(x-1)^2 and g(x)=x^1/2. Now, to deterrmine the value for gof(x) we first have to find f(x) and substitute the result we get as the x value in g(x).

Now we know that f(x) = (x-1)^2

Also, g(x) = x^1/2

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

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

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

=(x-1)

**Therefore g(f(x)) = gof(x) = (x-1)**

The composition of the functions g and f could be written as:

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

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

We'll substitute 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|**

f(x) = (x-1)^2 and g(x) = x^(1/2.

To find (gof)(x).

g(x) = x^(1/2).

We substitute f(x) in place of x i g(x) to obtain (gof):

Therefore (gof)(y) = { (x-1)^2}^(1/2) = (x-1)

(gof)(x) = x-1.

Therefore the composition (gof) = x-1.