Question

If g(x)=1-x and h(x)=x/(x-1) then g(h(x))/h(g(x)) is

Answer 1

Answer:

option A

Step-by-step explanation:

Answer 2

Given:

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

To find:

The value of g(h(x))/h(g(x))

Solution:

The value of g(h(x))/h(g(x)) is h(x)/g(x).

We can find the value by following the given process-

We know that to obtain g(h(x)), we will have to substitute h(x) as x in g(x).

Similarly, to obtain h(g(x)), we need to substitute h(x) as x in h(x).

The value of g(x)=1-x

The value of h(x)= x/(x-1)

So, the value of g(h(x))=1-h(x)

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

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

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

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

Now, the value of h(g(x))=g(x)/(g(x)-1)

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

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

=(1-x)/-x

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

The value of g(h(x))/h(g(x)) can be obtained by putting the values of g(h(x)) and h(g(x)).

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

= -1/(x-1)×(-x)/(1-x)

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

On observing the obtained value, we get

g(h(x))/h(g(x))=h(x)×1/g(x)

g(h(x))/h(g(x))=h(x)/g(x)

Therefore, the value of g(h(x))/h(g(x)) is h(x)/g(x) or x/(x-1)(1-x).