+752 Here are two functions:
If f(10) - g(10) = 10, what is the value of k?
+9466 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
+2441 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!
+2441 Wow! We approached the problem in an identical manner, and we explained our method nearly verbatim.
