SAT Math : How to find f(x)
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Example Questions
Example Question #1 :How To Find F(X)
Iff(x) =x2– 5 for all valuesxandf(a) = 4, what is one possible value ofa?
14
1
8
11
3
3
Using the defined function,f(a) will produce the same result when substituted forx:
f(a) =a2– 5
Setting this equal to 4, you can solve fora:
a2– 5 = 4
a2= 9
a= –3 or 3
Example Question #1 :How To Find F(X)
If the functiongis defined byg(x) = 4x+ 5, then 2g(x) – 3 =
8x+ 2
4x+ 2
6x+ 7
8x+ 7
6x+ 2
8x+ 7
The functiong(x) is equal to 4x+ 5, and the notation 2g(x)问你s to multiply the entire function by 2. 2(4x+ 5) = 8x+ 10. We then subtract 3, the second part of the new equation, to get 8x+ 7.
Example Question #261 :Algebra
Iff(x) =x2+ 5xandg(x) = 2, what isf(g(4))?
39
2
14
36
4
14
First you must find whatg(4) is. The definition ofg(x) tells you that the function is always equal to 2, regardless of what “x” is. Plugging 2 intof(x), we get 22+ 5(2) = 14.
Example Question #2 :How To Find F(X)
f(a) =1/3(a3+ 5a– 15)
Finda= 3.
19
1
9
3
27
9
Substitute 3 for all a.
(1/3) * (33+ 5(3) – 15)
(1/3) * (27 + 15 – 15)
(1/3) * (27) = 9
Example Question #2 :How To Find F(X)
Evaluatef(g(6)) given thatf(x) =x2– 6 andg(x) = –(1/2)x– 5
–8
50
58
–25
30
58
Begin by solvingg(6) first.
g(6) = –(1/2)(6) – 5
g(6) = –3 – 5
g(6) = –8
We substitutef(–8)
f(–8) = (–8)2– 6
f(–8) = 64 – 6
f(–8) = 58
Example Question #1 :How To Find F(X)
Iff(x) = |(x2– 175)|, what is the value off(–10) ?
15
275
–75
–275
75
75
Ifx= –10, then (x2– 175) = 100 – 175 = –75. But the sign |x| means the absolute value ofx. Absolute values are always positive.
|–75| = 75
Example Question #2 :How To Find F(X)
If f(x)= 2x² + 5x – 3, then what is f(–2)?
7
–1
–5
–21
–5
By plugging in –2 for x and evaluating, the answer becomes 8 – 10 – 3 = -5.
Example Question #8 :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 #3 :How To Find F(X)
f(x) = 2x2+ x – 3 and g(y) = 2y – 7. What is f(g(4))?
0
33
42
57
-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*
4*
5*
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.
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