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

$h(x)=\frac{10}{x}-3,g(x)=3x-2_{}$

Now,

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

Now hg(4) will be

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

So, the required answer is -5.