Question

Find (gof)(x) when f(x)=sqrt x+3 and g(x)= x^2+2/x

Answer 1

`(gof) (x) =\frac {(x+3)^{(3)/(2)}+2}{\sqrt {x + 3}}`

Explanation:

Given : Function
`f(x)=\sqrt {x+3}` and
`g(x)=x^2+(2)/(x)`

To find : The value of (gof)(x) ?

Solution :

We know that,

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

Substituting the values,

`(gof) (x) = g(\sqrt {x+3})`

`(gof) (x) =(\sqrt {x + 3})^2+ \frac {2} {\sqrt {x + 3}}`

`(gof) (x) =(x + 3) + \frac {2} {\sqrt {x + 3}}`

`(gof) (x) =\frac {(x+3)(\sqrt {x + 3})+2} {\sqrt {x + 3}}`

`(gof) (x) =\frac {(x+3)^{(3)/(2)}+2}{\sqrt {x + 3}}`