SAT Math : SAT Mathematics
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Example Question #2791 : Sat Mathematics
If 7y = 4x - 12, then x =
Adding 12 to both sides and dividing by 4 yields (7y+12)/4.
Example Question #3 : Algebraic Functions
If F(x) = 2x2 + 3 and G(x) = x – 3, what is F(G(x))?
2x2 – 12x +21
6x2 – 12x
2x2 + 12x +18
2x2
6x2 + 5x
2x2 – 12x +21
A composite function substitutes one function into another function and then simplifies the resulting expression. F(G(x)) means the G(x) gets put into F(x).
F(G(x)) = 2(x – 3)2 + 3 = 2(x2 – 6x +9) + 3 = 2x2 – 12x + 18 + 3 = 2x2 – 12x + 21
G(F(x)) = (2x2 +3) – 3 = 2x2
Example Question #2 : Algebraic Functions
If a(x) = 2x3 + x, and b(x) = –2x, what is a(b(2))?
503
–132
–503
132
128
–132
When functions are set up within other functions like in this problem, the function closest to the given variable is performed first. The value obtained from this function is then plugged in as the variable in the outside function. Since b(x) = –2x, and x = 2, the value we obtain from b(x) is –4. We then plug this value in for x in the a(x) function. So a(x) then becomes 2(–43) + (–4), which equals –132.
Example Question #2 : How To Find F(X)
Let F(x) = x3 + 2x2 – 3 and G(x) = x + 5. Find F(G(x))
x3 + x2 + 2
x3 + 2x2 + x + 2
x3 + x2 + x + 8
x3 + 17x2 + 95x + 172
x3 + 2x2 – x – 8
x3 + 17x2 + 95x + 172
F(G(x)) is a composite function where the expression G(x) is substituted in for x in F(x)
F(G(x)) = (x + 5)3 + 2(x + 5)2 – 3 = x3 + 17x2 + 95x + 172
G(F(x)) = x3 + x2 + 2
F(x) – G(x) = x3 + 2x2 – x – 8
F(x) + G(x) = x3 + 2x2 + x + 2
Example Question #2 : Algebraic Functions
What is the value of xy2(xy – 3xy) given that x = –3 and y = 7?
3565
–2881
–6174
2881
–6174
Evaluating yields –6174.
–147(–21 + 63) =
–147 * 42 = –6174
Example Question #1 : How To Find F(X)
Find 
Alternatively, we can find that 
Example Question #1182 : Algebra
It takes no more than 40 minutes to run a race, but at least 30 minutes. What equation will model this in m minutes?
If we take the mean number of minutes to be 35, then we need an equation which is less than 5 from either side of 35. If we subtract 35 from 
Example Question #2791 : Sat Mathematics
If 
Example Question #2792 : Sat Mathematics
If 
The number in the parentheses is what goes into the function.
For the function 
Example Question #423 : Algebra
A function F is defined as follows:
for x2 > 1, F(x) = 4x2 + 2x – 2
for x2 < 1, F(x) = 4x2 – 2x + 2
What is the value of F(1/2)?
For F(1/2), x2=1/4, which is less than 1, so we use the bottom equation to solve. This gives F(1/2)= 4(1/2)2 – 2(1/2) + 2 = 1 – 1 + 2 = 2
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