SOLUTION: please help me solve h(f(6)) if h(x)= -x^2 + 6x f(x)= 7x - 40

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Question 72616: please help me solve h(f(6))
if
h(x)= -x^2 + 6x
f(x)= 7x - 40

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
First of all find f(6) by going to the original definition for f(x) and then replacing every
x by 6 and then simplifying the result.
.
You were given that
.
f(x) = 7*x - 40
.
Then to find f(6) you replace every x in the equation for f(x) by 6 to get:
.
f(6) = 7*6 - 40
.
And you simplify the right side to get:
.
f(6) = 42 - 40 = 2
.
So now you know that f(6) = 2
.
Next you are asked to find h(f(6)) given that
.
h%28x%29+=+-x%5E2+%2B+6x
.
To find h(f(6)) you just replace every x in h(x) with f(6). The result would be:
.
h%28f%286%29%29+=+-%28f%286%29%29%5E2+%2B+6%2A%28f%286%29%29
.
But on the right side you can substitute for f(6) its value which we found to be +2. If
you do your equation becomes:
.
h%28f%286%29%29+=+-%282%29%5E2+%2B+6%2A2
.
and the right side simplifies to:
.
h%28f%286%29%29+=+-4+%2B+12+=+8
.
So the answer to your problem is:
.
h%28f%286%29%29+=+8
.
Hope this helps you to better understand the way to work problems such as these.