What is 3 times 3

Question

Let f(x) = x + 8 and g(x) = x2 − 6x − 7. Find f(g(2)).

Answer 1

Mark M's solution is an excellent one, however, there is another approach to solving this problem:

 

First, determine f(g(x)) by replacing x in f(x) with g(x):

 

f(x) = x + 8

f(g(x)) = (x² - 6x - 7) + 8

 

Simplify to obtain:

f(g(x)) = x² - 6x + 1

 

Now, we can find f(g(2)) by substituting a value of 2 in for each x in our new function:

f(g(2)) = (2)² - 6(2) + 1

f(g(2)) = 4 - 12 + 1

f(g(2)) = -7

 

I hope this helps!

Answer 2

First, find g(2):   g(x) = x² - 6x - 7

                             g(2) = 2² - 6(2) - 7 = -15

 

So, since f(x) = x + 8, f(g(2)) = f(-15) = -15 + 8 = -7