1. If $f(x) = x^2 - 1$ and $g(x) = x + 7,$ evaluate $f(g(7)) + g(f(3)).$
2. Suppose $f(x)=\frac{3}{2-x}$. If $g(x)=\frac{1}{f^{-1}(x)}+9$, find $g(3)$.
3. For what value of does the equation represent a circle of radius 6?
4. The graph of $y=ax^2+bx+c$ is given below, where $a$, $b$, and $c$ are integers. Find $a-b+c$.
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+1252 f(g(7))+g(f(3)). Seems complex at first.
However, we can evaluate g(7), which is 7+7 = 14, and now we can find f(14)
Also, we can evaluate f(3), which is 3^2-1=8, and now we can find g(8).
f(14)=14^2-1=195 and g(8)=8+7=15.
Now we have 195+15 which equals 210.
You are very welcome!
:P
+9488 2. Suppose f(x)=32−x . If g(x)=1f−1(x)+9 , find g(3) .
Let's find f-1(x) by setting y = f(x) and solving for x .
y = 32−x y(2−x) = 3andx≠2 2−x = 3y −x = −2+3y x = 2−3y
So we know...
f−1(x) = 2−3x
And we can substitute this in for f-1(x) in the equation for g(x)
g(x) = 1f−1(x)+9 g(x) = 12−3x+9 g(3) = 12−33+9 g(3) = 12−1+9 g(3) = 1+9 g(3) = 10_
