Question

If g(x)=x-3 and h(x)=\sqrt(x), find (goh) (25)?

Answer 1

`\bf \begin{cases} g(x)=x-3\\ h(x)=√(x)\\ (g\circ h)(x)=g(~~h(x)~~)\\ (g\circ h)(25)=g(~~h(25)~~) \end{cases} \\\\\\ h(25)=√((25))\implies \boxed{h(25)=5} \\\\\\ (g\circ h)(25)\implies g(~~h(25)~~)\implies g\left(~~\boxed{5}~~ \right)=(5)-3\implies g(5)=2`

Answer 2

The 'o' notation means function composition. In this case
(g o h)(x) = g(h(x))

The inner function h(x) goes first. Replace x with 25 and simplify to get
h(x) = sqrt(x)
h(25) = sqrt(25)
h(25) = 5

Therefore,
(g o h)(25) = g(h(25)) = g(5)

Now we compute g(5)

g(x) = x-3
g(5) = 5-3
g(5) = 2

The answer is 2