Question

If tex2html_wrap_inline35 and g(x)=x-1, let h(x)=f(g(x)).

Find h(x).
What is the domain of h(x)?
Find h(2) and h(0).

Answer 1

Given :

`f(x)=√(x)`

`g(x)=x-1`

`h(x)=f(g(x))`

To Find :

Find h(x).

What is the domain of h(x).

Find h(2) and h(0).

Solution :

a )

Now , h(x) is given by :

`h(x)=f(x-1)\\\\h(x)=√(x-1)`

b )

We know , square root of negative number is not defined .

So, x-1 ≥ 0

x ≥ 1

Therefore , the domain of h(x) is [ 1 , ∞ ) .

c )

`h(2)=√(2-1)=1`

Since , domain of h(x) is [ 1 , ∞ ) .

Therefore , function has no value for 0 .

Hence , this is the required solution .