Question

Which expression is equivalent to (g*h)(5)?

Answer 1

For this case, we must perform a composition of functions.

Let two functions, f(x) and g(x). To find
`(f_ {0} g)` we calculate
`f (g (x)`, that is, replace g (x) in f (x).

So, if we have:

`h (x) = x-7\\g (x) = x ^ 2`

And we want to find
`(g_ {0} h) (x)`. We make:

`g (h (x)) = (x-7) ^ 2`

if we want the composite function evaluated at 5, we substitute
`x = 5`

`g (h (5)) = (5-7) ^ 2`

Answer:

`g (h (5)) = (5-7) ^ 2`

Option A

Answer 2

Answer:(5-7)²

Step-by-step explanation: as h(x)=x-7 and g(x)=x²

so, goh(x)=g(h(x))

=g(x-7)

=(x-7)²

hence, goh(5)=(5-7)²