00:01
Given f of x equals 3x and g of x equals 8 times x squared plus 1.
00:09
Find the following expressions when f of g and x is going to be 4.
00:17
So first thing we're going to do is write this as f of g of 4 because these are equal to the same thing.
00:28
So we're going to substitute x in our g equation and whatever we get for g is then going to be substituted into our f.
00:38
So this is going to look like 8 times 4 squared plus 1.
00:48
So doing order of operations this is going to be 8 times 16 plus 1.
00:56
16 times 8 is going to be 128 plus 1.
01:02
So this is going to be 129.
01:05
We're then going to take this, this is what our g of 4 is equal to.
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We're then going to substitute this into our f of x equation.
01:15
So f of g of 4 is going to equal 3 times 129.
01:27
So 3 times 129 is going to bring us to 387.
01:37
So that is going to be the answer for a.
01:40
Next up we have g of f of 2.
01:52
Same concept.
01:53
F of 2 is going to be f of x equals 3 times 2.
02:01
So that is going to be equal to 6.
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We're then going to plug that in to our g equation.
02:07
So 8 times 6 squared plus 1.
02:12
6 squared is 6 times 6 which is 36 plus 1 times 8.
02:20
36 times 8 is going to be 288 plus 1...