Suppose a(x) = 3x - 7 and b(x) = 2 - x^3. Find a(b(3)) - b(a(3)).
the answer is -76
you got it wrong the answer must be negative
True -76
Ah, working with functions, I see. Let's break it down step by step with a little dose of humor, shall we?
First, let's calculate b(3). Plug 3 into b(x) and stand back while I unveil the result: b(3) = 2 - 3^3 = 2 - 27 = -25.
Now, let's move on to a(b(3)). According to our calculations above, b(3) = -25. Now it's time to give a little spin to a(x), which is 3x - 7. Inserting b(3) into a(x), we get a(-25) = 3(-25) - 7. And after a bit of math magic: a(-25) = -75 - 7 = -82.
Finally, let's calculate b(a(3)). Plugging 3 into a(x), we get a(3) = 3(3) - 7 = 9 - 7 = 2. And applying this result to b(x): b(a(3)) = b(2) = 2 - 2^3 = 2 - 8 = -6.
Now, we're ready to find the grand finale: a(b(3)) - b(a(3)) = -82 - (-6) = -82 + 6 = -76.
There you go, my mathematical comedic friend! a(b(3)) - b(a(3)) equals -76!
To find a(b(3)) and b(a(3)), we need to substitute 3 into the respective functions and simplify. Let's start with a(b(3)):
a(b(3)) means we first need to find the value of b(3), and then substitute that result into function a.
To find b(3), we substitute 3 into the function b(x):
b(x) = 2 - x^3
b(3) = 2 - 3^3 = 2 - 27 = -25
Now, we substitute the value of -25 into function a(x):
a(x) = 3x - 7
a(b(3)) = 3*(-25) - 7 = -75 - 7 = -82
Next, let's find b(a(3)):
b(a(3)) means we first need to find the value of a(3), and then substitute that result into function b.
To find a(3), we substitute 3 into the function a(x):
a(x) = 3x - 7
a(3) = 3*3 - 7 = 9 - 7 = 2
Now, we substitute the value of 2 into function b(x):
b(x) = 2 - x^3
b(a(3)) = 2 - (2^3) = 2 - 8 = -6
Finally, we can compute a(b(3)) - b(a(3)):
a(b(3)) - b(a(3)) = -82 - (-6) = -82 + 6 = -76
Therefore, a(b(3)) - b(a(3)) equals -76.
nice job
I will do one of the components, you do the other , then subtract them
a(x) = 3x - 7 and b(x) = 2 - x^3
a(b(3))
= a(2-3^3)
= a(-25)
= 3(25) - 7 = 68