Question

HELP!!
let g(x)=5x-2 and h(x)= x^2 +1. Find (h o g) (-1)

Answer 1

To find the value of (h o g)(-1), first calculate g(-1) which is -7 and then evaluate h(-7), which results in 50.

Step-by-step explanation:

To find (h o g)(-1), you need to do a two-step process. First, evaluate g(-1), which is the function g(x) with x replaced by -1. According to the given function g(x) = 5x - 2, when you plug in -1 you get:

g(-1) = 5(-1) - 2

= -5 - 2

= -7

Now, take this result and plug it into the function h(x), so you compute h(g(-1)), which is equivalent to h(-7). Given h(x) = x² + 1, you get:

h(-7) = (-7)² + 1

= 49 + 1

= 50

Therefore, (h o g)(-1) = 50.

Answer 2

(h o g)(-1)) = 50

Step-by-step explanation:

Here, the functions are defined as

g(x) = 5x -2

`h(x)  = x^(2)  + 1`

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) =
`(5x-2)^(2)  + 1`

⇒
`h(g(x))  = (25x^(2)  + 4 - 20x)+ 1 = 25x^(2)  + 5 - 20x`

Putting x = -1 in the above expression,

`h(g(-1))  = 25(-1)^(2)  + 5 - 20(-1)\\= 25 + 5 + 20= 50`

Hence, h(g(-1)) = 50 or

(h o g)(-1)) = 50