Question

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

Answer 1

Given :

$f(x)=\sqrt{x}$

$g(x)=x-1$

$h(x)=f(g(x))$

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 :

$h(x)=f(x-1)\\\\h(x)=\sqrt{x-1}$

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 )

$h(2)=\sqrt{2-1}=1$

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

Therefore , function has no value for 0 .

Hence , this is the required solution .