Since the expressions for f(x) and g(x) are already given, f(g(2)) means to substitute the value of 2 to the expression of g(x), then further substituting the obtained value of g(2) into the expression of f(x). This is shown below:
f(x) = x + 8
g(x) = x^2 - 6x - 7
f(g(x) = x^2 - 6x - 7 + 8
f(g(2)) = 2^2 - 6(2) + 1
f(g(2)) = 4 - 12 + 1
f(g(2)) = -7
Therefore, the correct answer is -7.
bellamore
Middle SchoolMathematics 5+3 pts
x (.60) + 60 (.15) = (x+60) .50
distribute
.60x +9 = .5x +30
subtract .5x from each side
.1x +9 = 30
subtract 9 from each side
.1x = 21
divide by .1
x = 210
You will need 210 gallons of 60% antifreeze
Remark
The way this is written I would assume that it means 4*f(x) = x. That may not be entirely the correct assumption to be made.
Step One
Replace f(x) by 4f(x)
4*f(x) = x
Step two
Divide both steps by 4
f(x) = x/4 or (1/4)x
The slope is now 1/4
Discussion
A is incorrect.
The slope has been changed.
B is incorrect
The slope has been changed to 1/4 and the y intercept is still 0
C looks to be the right answer.
D The y intercept is still zero.
Comment
The question is a little hard to interpret. I've read it literally. That means that I have taken the question to mean that only f(x) was altered. If however, the right side was multiplied by 4 as well (as should be done), then the answer is A same slope same intercept. That's because the 4s on the left and right cancel, and the original equation results. I'm going to pick C but don't be surprised if it is A
C <<<<<answer
