Question

I have a Algebra 2 question

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

find g(f(4))

Answer 1

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.

Answer 2

g(f(4)) = 571

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