Question

Composition of function check for understanding

Answer 1

The composite functions are (g o h)(t) = 2t^2 - 11, g(h(a)) = 8a^3 and  (g o h)(t) = 4n + 7

How to determine the composite functions?

Functions g(t) and h(t)

We have:

g(t) = 2t - 5

h(t) = t^2 - 3

The function (g o h)(t) is calculated as:

(g o h)(t) = g(h(t))

This gives

(g o h)(t) = 2(t^2 - 3) - 5

Evaluate

(g o h)(t) = 2t^2 - 6 - 5

(g o h)(t) = 2t^2 - 11

Functions g(a) and h(a)

We have:

h(a) = 2a

g(a) = a^3

The function g(h(a)) is calculated as:

g(h(a)) = (2a)^3

Evaluate

g(h(a)) = 8a^3

Functions g(n) and h(n)

We have:

g(n) = 2n + 5

h(n) = 2n + 1

The function (g o h)(n) is calculated as:

(g o h)(n) = g(h(n))

This gives

(g o h)(t) = 2(2n + 1) + 5

Evaluate

(g o h)(t) = 4n + 2 + 5

(g o h)(t) = 4n + 7

Hence, the composite functions are (g o h)(t) = 2t^2 - 11, g(h(a)) = 8a^3 and  (g o h)(t) = 4n + 7

Read more about composite functions at

brainly.com/question/20379727

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