Question

If f(x) =1/2 x + 2 and g(x) = −3x − 1, find g[f(4)].
−19

11

−13

−11

Answer 1

f(4) substitute in f(x)....

Answer 2

Yes

Answer 3

substitute the value of f(4) in g(x)

Answer 4

You can do this in at least 2 different ways. One is to find the value of f(4), then find the value of g(f(4)). The other is to figure out what g(f(x)) is, and substitute 4 for x.

Answer 5

Which would you like to do?

Answer 6

1st

Answer 7

Okay. \[f(x) =\frac{1}{2} x + 2\]\[f(4) = \frac{1}{2}(4)+2 = \]

Answer 8

f(4)=4

Answer 9

?

Answer 10

is that an answer, or a prayer? :-)

Answer 11

So the answer is -13

Answer 12

yes, the answer is -13.

I'll quickly do it the other way, which if you had to compute g(f(x)) a bunch of times would be more convenient:

\[f(x) = \frac{1}{2}x + 2\]
\[g(x) = -3x-1\]
\[g(\frac{1}{2}x+2) = -3(\frac{1}{2}x+2) - 1 = -\frac{3}{2}x-6-1 = -\frac{3}{2}x-7\]
so \[g(f(x)) = -\frac{3}{2}x-7\]and \[g(f(4)) = -\frac{3}{2}(4)-7 = -13\]

Answer 13

I was right Thankyou