ALgebra 2 functions work

Question

f(x)= -3x+4 and g(x)= x +7 what is the value of g(f(2)) ?

Answer 1

Hi Misha,

To evaluate functional compositions, we need to evaluate functions from the inside first, and move outside. Since the innermost function is f(2), we evaluate that first:

We know that f( x ) = -3x + 4, so all we need to do is substitute 2 for x, which gives us the following:

f ( 2 ) = -3 (2) + 4

Which, after multiplication and addition, gives us

f ( 2 ) = -2

Now, knowing the value of f ( 2 ), we can substitute again -- this time, we replace f ( 2 ) with -2 in our composed function. So, g ( f ( 2 ) ) becomes g ( - 2 ).

Now, as before, we simply plug into our equation -- this time, it is g( x ), which gives us:

g ( -2 ) = -2 + 7

g ( -2 ) = 5

So, we have shown that g ( f ( 2 ) ) = 5.

Hope this helps!

Best,

Nate

Answer 2

f(x)= -3x+4 and g(x)= x +7 what is the value of g(f(2))

f(2)=-3(2)+4=-6+4=-2

g(f(2))=g(-2)=-2+7=5