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Here are two functions:

If f(10) - g(10) = 10, what is the value of k?

 Jul 30, 2017
 #1
avatar+7352 
+4

f( x )  =  3x2 – 2x + 4                    To find  f(10)  , replace every instance of  x  with  10 .

f(10)  =  3(10)2 – 2(10) + 4            Simplify.

f(10)  =  300 – 20 + 4

f(10)  =  284

 

g( x )  =    x2 – kx – 6                    To find  g(10)  , replace every instance of  x  with  10 .

g(10)  =  (10)2 – k(10) – 6              Simplify.

g(10)  =  100 –10k – 6

g(10)  =  94 – 10k

 

f(10) – g(10)  =  10                        Replace  f(10)  with 284  . Replace  g(10)  with  94 – 10k  .

284 – (94 – 10k)  =  10                 Now solve for k. Distribute the  -1  to both terms in parenthesees.

284 – 94 + 10k  =  10                  Combine  284  and  -94  .

190 + 10k  =  10                          Subtract  190  from both sides.

10k  =  -180                                 Divide both sides by  10  .

k  =  -18

 Jul 30, 2017
 #2
avatar+2340 
+2

Ok, answering this question requires some knowledge of functions. 

 

\(f(x)=3x^2-2x+4\)

\(g(x)=x^2-kx-6\)

 

When the question asks what is f(10)-g(10), the question is asking what the functions equal to when x=10.

 

Let's do just that first. I'll evaluate them separately.

 

\(f(x)=3x^2-2x+4\) Evaluate the function for f(10), which means make all instances of x into a 10.
\(f(10)=3*10^2-2*10+4\) We must be mindful about our order of operations here. First, do the exponent first.
\(f(10)=3*100-2*10+4\) Let's evaluate all instances of multiplication first.
\(f(10)=300-20+4\) Do the subtraction and addition.
\(f(10)=284\)  
   

 

Now, let's evaluate the other function.

 

\(g(x)=x^2-kx-6\) Again, replace all instances of x with 10.
\(g(10)=10^2-k*10-6\) Evaluate exponents first to abide with order of operations.
\(g(10)=100-10k-6\) Combine the only set of like terms, 100 and -6.
\(g(10)=94-10k\)  
   

 

Ok, now we have to do f(10)-g(10)=10:

 

\(f(10)-g(10)=10\) Replace the calculated values for f(10)-g(10)
\(284-(94-10k)=10\) Distribute the negative sign into the parentheses.
\(284-94+10k=10\) Do 284-94 to simplify the lefthand side. 
\(190+10k=10\) Subtract 190 on both sides of the equation.
\(10k=-180\) Divide by 10 on both sides.
\(k=-18\)  
   

 

Ok, I am done now! 

 Jul 30, 2017
 #3
avatar+2340 
+1

Wow! We approached the problem in an identical manner, and we explained our method nearly verbatim.

TheXSquaredFactor  Jul 30, 2017
 #4
avatar+7352 
+2

And...we posted it at almost the exact same time, LOL smiley

hectictar  Jul 30, 2017

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