[GMAT math practice question]
f(x) has the properties, f(x+y) = x + f(y) and f(0) = 5. What is the value of f(100)?
A. 95
B. 100
C. 105
D. 120
E. 135
f(x) has the properties, f(x+y) = x + f(y) and f(0) = 5. Wha
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- Max@Math Revolution
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$$\left( * \right)\,\,\,\left\{ \matrix{Max@Math Revolution wrote:[GMAT math practice question]
f(x) has the properties, f(x+y) = x + f(y) and f(0) = 5. What is the value of f(100)?
A. 95
B. 100
C. 105
D. 120
E. 135
f\left( 0 \right) = 5 \hfill \cr
f\left( {x + y} \right) = x + f\left( y \right) \hfill \cr} \right.$$
$$? = f\left( {100} \right)$$
$${\text{Take}}\,\,\left( {x,y} \right) = \left( {100,0} \right)\,\,\,\,\, \Rightarrow \,\,\,\,? = f\left( {100 + 0} \right)\,\,\mathop = \limits^{\left( * \right)} \,\,100 + f\left( 0 \right)\,\,\mathop = \limits^{\left( * \right)} \,\,105$$
We follow the notations and rationale taught in the GMATH method.
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Fabio.
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Given: f(x+y) = x + f(y)Max@Math Revolution wrote:[GMAT math practice question]
f(x) has the properties, f(x+y) = x + f(y) and f(0) = 5. What is the value of f(100)?
A. 95
B. 100
C. 105
D. 120
E. 135
What is the value of f(100)?
We need to somehow use the fact that f(0) = 5 to help us determine the value of f(100).
Notice that we can rewrite 100 as 100 + 0
According to our the function f, we know that: f(100 + 0) = 100 + f(0)
= 100 + 5
= 105
Answer: C
Cheers,
Brent
- Max@Math Revolution
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=>
Using f(x +y ) = x + f(y) yields
f(x) = f(x+0) = x + f(0)
Now, using f(0) = 5 yields
f(x) = x + 5.
Therefore,
f(100) = 100 + 5 = 105.
Therefore, the answer is C.
Answer: C
Using f(x +y ) = x + f(y) yields
f(x) = f(x+0) = x + f(0)
Now, using f(0) = 5 yields
f(x) = x + 5.
Therefore,
f(100) = 100 + 5 = 105.
Therefore, the answer is C.
Answer: C
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