Answer:
13) [tex] (h - f)(3) = 10 [/tex]
14)[tex] (h \circ g)(5) = 695 [/tex]
Step-by-step explanation:
To find the function values, let's substitute the given values into the respective functions:
Problem 13: [tex] (h - f)(3) [/tex]
[tex] (h - f)(3) = h(3) - f(3) [/tex]
Given:
[tex] f(x) = 1 - 6x [/tex]
[tex] h(x) = 2x^2 - 9x + 2 [/tex]
Evaluate [tex] h(3) [/tex]:
[tex] h(3) = 2(3)^2 - 9(3) + 2 [/tex]
[tex] h(3) = 18 - 27 + 2 [/tex]
[tex] h(3) = -7 [/tex]
Evaluate [tex] f(3) [/tex]:
[tex] f(3) = 1 - 6(3) [/tex]
[tex] f(3) = 1 - 18 [/tex]
[tex] f(3) = -17 [/tex]
Now, find [tex] (h - f)(3) [/tex]:
[tex] (h - f)(3) = h(3) - f(3) [/tex]
[tex] = (-7) - (-17) [/tex]
[tex] = 10 [/tex]
So, [tex] (h - f)(3) = 10 [/tex].
Problem 14: [tex] (h \circ g)(5) [/tex]
[tex] (h \circ g)(5) = h(g(5)) [/tex]
Given:
[tex] g(x) = x^2 - 4 [/tex]
[tex] h(x) = 2x^2 - 9x + 2 [/tex]
Evaluate [tex] g(5) [/tex]:
[tex] g(5) = (5)^2 - 4 [/tex]
[tex] g(5) = 25 - 4 [/tex]
[tex] g(5) = 21 [/tex]
Now, find [tex] (h \circ g)(5) [/tex]:
[tex] (h \circ g)(5) = h(g(5)) [/tex]
[tex] = h(21) [/tex]
Evaluate [tex] h(21) [/tex]:
[tex] h(21) = 2(21)^2 - 9(21) + 2 [/tex]
[tex] h(21) = 882 - 189 + 2 [/tex]
[tex] h(21) = 695 [/tex]
So, [tex] (h \circ g)(5) = 695 [/tex].