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Question: Find f(4)f(4), if 3f(x)+4f(1x)=x+43f(x)+4f(x1)=x+4.
a. 8
b. 16
c. -1
d. -16
Solution:
The simplest way to solve such functions is to consider them variables and make linear equations.
We are given that 3f(x)+4f(1x)=x+43f(x)+4f(x1)=x+4 and we need to find f(4)f(4)
Let's put x = 4, we get 3f(4)+4f(14)=83f(4)+4f(41)=8 ................. Equation 1.
Now, let's put x = 1441, we get 3f(14)+4f(4)=1743f(41)+4f(4)=417..... .... Equation 2.
We have the required function, i.e. f(4)f(4), in both equations. Our goal should be to eliminate the other variable only. For that, we can do the following mathematical functions: Equation 1 × 3 − × 3 − Equation 2× 42× 4.
We get, 9f(4)+12f(14)=24 & 16f(4)+12f(14)=179f(4)+12f(41)=24 & 16f(4)+12f(41)=17
Subtracting Equation 2 from Equation 1, we get
−7f(4)=7−7f(4)=7
f(4)=−1f(4)=−1
Answer c
a. 8
b. 16
c. -1
d. -16
Solution:
The simplest way to solve such functions is to consider them variables and make linear equations.
We are given that 3f(x)+4f(1x)=x+43f(x)+4f(x1)=x+4 and we need to find f(4)f(4)
Let's put x = 4, we get 3f(4)+4f(14)=83f(4)+4f(41)=8 ................. Equation 1.
Now, let's put x = 1441, we get 3f(14)+4f(4)=1743f(41)+4f(4)=417..... .... Equation 2.
We have the required function, i.e. f(4)f(4), in both equations. Our goal should be to eliminate the other variable only. For that, we can do the following mathematical functions: Equation 1 × 3 − × 3 − Equation 2× 42× 4.
We get, 9f(4)+12f(14)=24 & 16f(4)+12f(14)=179f(4)+12f(41)=24 & 16f(4)+12f(41)=17
Subtracting Equation 2 from Equation 1, we get
−7f(4)=7−7f(4)=7
f(4)=−1f(4)=−1
Answer c
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