Question

The functions h(x) and g(x) are defined as h(x)= ¹⁰/x -3 and g(x)=3x-2evaluate hg(4)

Answer 1

We will use the property

`(fg)(x)=f(x)g(x)`

Given data:

It is given that

`h(x)=(10)/(x)-3,g(x)=3x-2_{}`

Now,

`\begin{gathered} hg(x)=h(x)g(x) \\ =((10)/(x)-3)(3x-2) \\ =(10)/(x)(3x-2)-3(3x-2) \\ =30-(20)/(x)-9x+6 \\ =36-(20)/(x)-9x \end{gathered}`

Now hg(4) will be

`\begin{gathered} hg(4)=36-(20)/(4)-9(4) \\ =36-5-36 \\ =-5 \end{gathered}`

So, the required answer is -5.