To find [tex]\( f(-6) \)[/tex] and [tex]\( g(-4) \)[/tex] using the given functions, we will substitute the values of [tex]\( x \)[/tex] into each function.
First, let's find [tex]\( f(-6) \)[/tex] given [tex]\( f(x) = 2x + 4 \)[/tex]:
[tex]\[ f(-6) = 2(-6) + 4 \][/tex]
Now, let's simplify:
[tex]\[ f(-6) = -12 + 4 \][/tex]
[tex]\[ f(-6) = -8 \][/tex]
So, we have:
[tex]\[ f(-6) = -8 \][/tex]
Next, let's find [tex]\( g(-4) \)[/tex] given [tex]\( g(x) = 2x^3 + 6 \)[/tex]:
[tex]\[ g(-4) = 2(-4)^3 + 6 \][/tex]
Now, let's simplify:
[tex]\[ (-4)^3 = -64 \][/tex]
[tex]\[ g(-4) = 2(-64) + 6 \][/tex]
[tex]\[ g(-4) = -128 + 6 \][/tex]
[tex]\[ g(-4) = -122 \][/tex]
So, we have:
[tex]\[ g(-4) = -122 \][/tex]
Thus, the simplified answers are:
[tex]\[ f(-6) = -8 \][/tex]
[tex]\[ g(-4) = -122 \][/tex]