# f(x)= X^2 + X, h(x)= X/1-X....Find h(f(x)) in terms of X.

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Given the functions f(x) and h(x) such that:

f(x) = x^2 + x

h(x) = x / (1-x).

We need to find h(f(x))

To find h(f(x) we will substitute with f(x) in g(x).

h(f(x)) = h ( x^2 + x)

Now substitute with (x^2 + x) in h(x):

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

Now we will simplify.

Factor x from the numerator.

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

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

==>** h(f(x)) = -x(x+1)/ (x^2 +x -1) **

f(x)= x^2+x, h(x)= x/1-x. We are required find h(f(x)) in terms of x.

h(x) = 1/(1-x)

We form the composition of h(f(x)) . To do this we substiute f(x) in place of x.

Therefore h(f(x)) = 1/(1-f(x)). Now we substitute x^+x in place of f(x).

Therefore h(f(x)) = 1/{1-(x^2+x)} = 1/(1-x-x^2).

Therefore h(f(x)) = 1/(1-x-x^2).