The value of [tex](f\times g)(-2)[/tex] is 22
Explanation:
Given that the two functions are [tex]f(x)=-7x-3[/tex] and [tex]g(x)=\sqrt{x+6}[/tex]
We need to determine the value of [tex](f\times g)(-2)[/tex]
The value of [tex](f\times g)(-2)[/tex]:
To determine the value of [tex](f\times g)(-2)[/tex] , we shall first find the value of [tex](f\times g)(x)[/tex]
Thus, we have,
[tex](f\times g)(x)=f(x)\times g(x)[/tex]
Substituting the values, we get,
[tex](f\times g)(x)=(-7x-3)(\sqrt{x+6})[/tex]
Now, we shall find the value of [tex](f\times g)(-2)[/tex]
Substituting x = -2 in the equation [tex](f\times g)(x)=(-7x-3)(x+6)[/tex], we have,
[tex](f\times g)(-2)=(-7(-2)-3)(\sqrt{-2+6})[/tex]
Simplifying the values, we have,
[tex](f\times g)(-2)=(14-3)(\sqrt{4})[/tex]
[tex]=(11)(2)[/tex]
[tex]=22[/tex]
Thus, the value of [tex](f\times g)(-2)[/tex] is 22
