SAT Math : SAT Mathematics
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Example Question #4 : Algebraic Functions
Evaluate f(g(6)) given that f(x) = x2 – 6 and g(x) = –(1/2)x – 5
–8
–25
58
30
50
58
Begin by solving g(6) first.
g(6) = –(1/2)(6) – 5
g(6) = –3 – 5
g(6) = –8
We substitute f(–8)
f(–8) = (–8)2 – 6
f(–8) = 64 – 6
f(–8) = 58
Example Question #5 : Algebraic Functions
If f(x) = |(x2 – 175)|, what is the value of f(–10) ?
75
15
275
–275
–75
75
If x = –10, then (x2 – 175) = 100 – 175 = –75. But the sign |x| means the absolute value of x. Absolute values are always positive.
|–75| = 75
Example Question #4 : How To Find F(X)
If f(x)= 2x² + 5x – 3, then what is f(–2)?
–1
–21
–5
7
–5
By plugging in –2 for x and evaluating, the answer becomes 8 – 10 – 3 = -5.
Example Question #5 : How To Find F(X)
If f(x) = x² – 2 and g(x) = 3x + 5, what is f(g(x))?
9x² + 30x + 23
9x² + 30x + 25
9x² + 23
3x² – 1
9x² + 30x + 23
To find f(g(x) plug the equation for g(x) into equation f(x) in place of “x” so that you have: f(g(x)) = (3x + 5)² – 2.
Simplify: (3x + 5)(3x + 5) – 2
Use FOIL: 9x² + 30x + 25 – 2 = 9x² + 30x + 23
Example Question #7 : Algebraic Functions
f(x) = 2x2 + x – 3 and g(y) = 2y – 7. What is f(g(4))?
42
57
33
0
-33
0
To evaluate f(g(4)), one must first determine the value of g(4), then plug that into f(x).
g(4) = 2 x 4 – 7 = 1.
f(1) = 2 x 12 + 2 x 1 – 3 = 0.
Example Question #1 : How To Find F(X)
For all positive integers, let k* be defined by k* = (k-1)(k+2) . Which of the following is equal to 3*+4*?
6*
7*
5*
4*
5*
We can think of k❋ as the function f(k)=(k-1)(k+2), so 3❋+4❋is f(3)+f(4). When we plug 3 into the function, we find f(3)=(3-1)(3+2)=(2)(5)=10, and when we plug 4 into the function, we find f(4)=(4-1)(4+2)=(3)(6)=18, so f(3)+f(4)=10+18=28. The only answer choice that equals 28 is 5❋ which is f(5)=(5-1)(5+2)=(4)(7)=28.
Example Question #2751 : Sat Mathematics
If x must be an integer, which of the following could be the value of f(x)?
f(x) = 2x2 - 6
0
4
6
2
2
If f(x) = 2, then x will be 2. All other times x will yield a radical that cannot be reduced.
Example Question #11 : How To Find F(X)
The cost of a cell phone plan is $40 for the first 100 minutes of calls, and then 5 cents for each minute after. If the variable x is equal to the number of minutes used for calls in a month on that cell phone plan, what is the equation f(x) for the cost, in dollars, of the cell phone plan for calls during that month?
f(x) = 40 + 5x
f(x) = 40 + 0.05x
f(x) = 40 + 0.5x
f(x) = 40 + 0.5(x - 100)
f(x) = 40 + 0.05(x - 100)
f(x) = 40 + 0.05(x - 100)
40 dollars is the constant cost of the cell phone plan, regardless of minute usage for calls. We then add 5 cents, or 0.05 dollars, for every minute of calls over 100. Thus, we do not multiply 0.05 by x, but rather by (x - 100), since the 5 cent charge only applies to minutes used that are over the 100-minute barrier. For example, if you used 101 minutes for calls during the month, you would only pay the 5 cents for that 101st minute, making your cost for calls $40.05. Thus, the answer is 40 + 0.05(x - 100).
Example Question #2752 : Sat Mathematics
f(x) = 4x + 2
g(x) = 3x - 1
The two equations above define the functions f(x) = g(x). If f(d) = 2g(d) for some value of d, then what is the value of d?
1/2
3
3/2
2
-2
2
f(x) = 4x + 2
g(x) = 3x - 1
We have f(d) = 2g(d). We multiply each value in g(d) by 2.
4d + 2 = 2(3d - 1) (Distribute the 2 in the parentheses by multiplying each value in them by 2.)
4d + 2 = 6d - 2 (Add 2 to both sides.)
4d + 4 = 6d (Subtract 4d from both sides.)
4 = 2d (Divide both sides by 2.)
2 = d
We can plug that back in to double check.
4(2) + 2 = 6(2) - 2
8 + 2 = 12 - 2
10 = 10
Example Question #2753 : Sat Mathematics
The function f, where f(x) = x2 + 6x + 8, is related to function g, where g(x) = 5 f(x-2). What is g(3)?
150
175
125
50
75
75
Doing things in an orderly way is a friend to the test-taker.
g(3) = 5 f(3-2)
= 5 f(1)
= 5 [ 12 + 6∙1 + 8]
= 5 [ 1 + 6 + 8]
= 5 [ 15]
= 75
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