Answer:
(h o g)(-1)) = 50
Step-by-step explanation:
Here, the functions are defined as
g(x) = 5x -2
[tex]h(x) = x^{2} + 1[/tex]
Now, (h 0 g) (x) is defined as the function h of g(x).
⇒ (h 0 g) (x) = h(g(x))
now, by definition of both functions:
h(g(x)) = h(5x-2) = [tex](5x-2)^{2} + 1[/tex]
⇒[tex]h(g(x)) = (25x^{2} + 4 - 20x)+ 1 = 25x^{2} + 5 - 20x[/tex]
Putting x = -1 in the above expression,
[tex]h(g(-1)) = 25(-1)^{2} + 5 - 20(-1)\\= 25 + 5 + 20= 50[/tex]
Hence, h(g(-1)) = 50 or
(h o g)(-1)) = 50
