Question

Given the following functions f(x) and g(x), solve f[g(6)] and select the correct answer below:

f(x) = 6x + 12

g(x) = x − 8

Answer 1

First, find g(6).
Then use that value in function f.

Answer 2

What is function g evaluated at x = 6?
g(x) = x - 8
g(6) = 6 - 8
g(6) = ?

Answer 3

-2 ?

Answer 4

So , the answer would be 0 because 6(-2)+12=0
Right ?

Answer 5

Correct.

Answer 6

Thank you so much ! Can I ask another one ?

Answer 7

f(g(x)) = f(x - 8) = 6(x - 8) + 12

f(g(2)) = 6(2 - 8) + 12 = 6(-6) + 12 = -12 + 12 = 0

Answer 8

You're welcome.
Yes, go ahead.

Answer 9

Given the following functions f(x) and g(x), solve f over g(−4) and select the correct answer below:

f(x) = 4x − 4

g(x) = x − 1

Answer 10

\(\dfrac{f}{g}(x) = \dfrac{f(x)}{g(x)} = \dfrac{4x - 4}{x - 1} = \dfrac{4(x - 1)}{x - 1} = 4\)

Since \(\dfrac{f}{g}(x) = 4\), no matter what x is, \(\dfrac{f}{g}(-4) = 4\)

Answer 11

So technically x=4 ?

Answer 12

No. In this problem, you were asked to find the value of the quotient of the
functions at x = -4.
For any value of x, the value of the quotient of the functions is 4, with only one exception, which is at x = 1. This division of functions is undefined at x = 1 because it involves division by zero. For all other values of x, the division of these two functions is 4.

Answer 13

@mathstudent55 factored a 4 out and was able to cancel x-1
so we don't have to evaluate when x = -4 anymore
we just have 4