Answer:
I'll go over the first two problems and you'll probably be able to do the rest on your own.
1.)
g(a) = 4a - 2
h(a) = -3a² - 2
Find (g○h)(a)
What (g○h)(x) mean is g( f(x) ). In this case, we have
(g○h)(a) so it's the same as g( f(a) ). All you do for this is plug in f(a) into every a that you see in g(a).
(g○h)(a) = g( f(a) )
(g○h)(a) = g( -3a² - 2 )
(g○h)(a) = 4(-3a² - 2) - 2
(g○h)(a) = -12a² - 10
2.)
g(n) = 2n - 3
f(n) = 2n³ + 2n²
(g○f)(n) = g( f(n) )
(g○f)(n) = g( 2n³ + 2n² )
(g○f)(n) = 2(2n³ + 2n²) - 3
(g○f)(n) = 4n³ + 4n² - 3
2x multiplies to all numbers:
2x x 8x3 = 16x4
2x x 6x2 = 12x3
2x x -10x = -20x2
Answer: 16x4 + 12x³ - 20x²
Hope this helps :)
Step-by-step explanation:
<u><em>f(a):</em></u>
So for this you simply plug in "a" as x, and this doesn't really do anything beside replace all values with x, so you just have the equation:
<u><em>2 f(a):</em></u>
So for this one, you want to represent f(a) using the equation it's equal to (5a + 4), and substitute it in for f(a). In doing so, you get the expression:
2*f(a) -> 2(5a + 4) -> 10a + 8
<u><em>f(2a):</em></u>
So this is very similar to the first question, although you will have to do some multiplication. So just plug in 2a as "x" to get the equation:
<u><em>f(a+2):</em></u>
Basically the same process, you plug in (a+2) as "x" and simplify:
<u><em>f(a) + f(2)</em></u>:
This is similar to the second question, and you simply want to replace the f(a) with the equation that represents it (5a + 4) and same thing for f(2) = 5(2) + 4