ANSWER
[tex]( f \circ \: g)( - 5)= -53[/tex]
EXPLANATION
The given functions are:
f(x) = -2x - 7 and g(x) = -4x + 3
[tex]( f \circ \: g)(x) = f(g(x))[/tex]
[tex]( f \circ \: g)(x) = f( - 4x + 3)[/tex]
[tex]( f \circ \: g)(x) = - 2( - 4x + 3) - 7[/tex]
Expand:
[tex]( f \circ \: g)(x) = 8x - 6 - 7[/tex]
[tex]( f \circ \: g)(x) = 8x - 13[/tex]
We substitute x=-5
[tex]( f \circ \: g)( - 5) = 8( - 5) - 13 = -53[/tex]
