Answer:
[tex]\sf h(5) = 2 [/tex]
Step-by-step explanation:
Given:
[tex]\sf f(x) = x - 1 [/tex]
[tex]\sf g(x) = -2x [/tex]
We can substitute these functions into the expression for [tex]\sf h(x) [/tex]:
[tex]\sf h(x) = -f(x + 2) - 2g(x - 3) [/tex]
First, let's find [tex]\sf f(x + 2) [/tex]:
[tex]\sf f(x + 2) = (x + 2) - 1 = x + 1 [/tex]
Now, let's find [tex]\sf g(x - 3) [/tex]:
[tex]\sf g(x - 3) = -2(x - 3) = -2x + 6 [/tex]
Now, substitute these expressions back into [tex]\sf h(x) [/tex]:
[tex]\sf h(x) = - (x + 1) - 2(-2x + 6) [/tex]
[tex]\sf h(x) = -x - 1 + 4x - 12 [/tex]
[tex]\sf h(x) = 3x - 13 [/tex]
Now, to find [tex]\sf h(5) [/tex], we substitute [tex]\sf x = 5 [/tex] into the expression for [tex]\sf h(x) [/tex]:
[tex]\sf h(5) = 3(5) - 13 [/tex]
[tex]\sf h(5) = 15 - 13 [/tex]
[tex]\sf h(5) = 2 [/tex]
So, the value of [tex]\sf h(5) [/tex] is [tex]\sf 2 [/tex].
