I have a Algebra 2 question

f (x) = 5x + 4 and g (x) = x^2 - 5

find g (f (4))

g (f (4)) = 571

Step-by-step explanation:

g (f (4))

We need to evaluate the function f at x=4

f (4) = 5*4 + 4

f (4) = 20+4

f (4) = 24

Now we have to evaluate the function g at 24

g (24) = 24^2 - 5

576 - 5

571

g (f (4)) = 571

Answer: 571

To get this answer, we first need to compute the value of f (4). This happens when we plug x = 4 into f (x)

f (x) = 5x + 4

f (4) = 5*4+4 ... each x replaced with 4

f (4) = 20+4

f (4) = 24

Now replace every 'x' in g (x) with f (4) like so

g (x) = x^2 - 5

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

g (f (4)) = (f (4)) ^2 - 5 ... every x replaced with f (4)

g (f (4)) = (24) ^2 - 5 ... see note below

g (f (4)) = 576 - 5

g (f (4)) = 571

note: the f (4) on the right hand side of that equation is replaced with 24, because we found earlier that f (4) = 24. In other words, f (4) is the same as 24.