1
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We’re asked to evaluate -2 × f(-6) + g(1).

2
00:00:06,434 --> 00:00:08,233
And they've defined – at least graphically –

3
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f(x) and g(x) here below.

4
00:00:10,702 --> 00:00:12,171
So let’s see how we can evaluate this.

5
00:00:12,171 --> 00:00:16,368
Well, to do this, we first have to figure out what f(-6) is.

6
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So our input into our function is -6.

7
00:00:19,548 --> 00:00:22,363
So we'll assume that's along the horizontal axis.

8
00:00:22,363 --> 00:00:24,037
So our input axis is -6.

9
00:00:24,037 --> 00:00:30,031
And, based on our function definition, f(-6) is 7.

10
00:00:30,031 --> 00:00:30,640
So this thing –

11
00:00:30,640 --> 00:00:31,571
Let me write this down.

12
00:00:31,571 --> 00:00:35,562
f(-6 ) = 7.

13
00:00:35,562 --> 00:00:39,999
And what is g(1)?

14
00:00:39,999 --> 00:00:42,706
Well, once again, here's our input axis.

15
00:00:42,706 --> 00:00:45,405
And then the function says that g(1) –

16
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which is right over there – is -5

17
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g(1) = -5.

18
00:00:52,101 --> 00:00:59,630
So this statement simplifies to -2 × f(-6), which is 7 ...

19
00:00:59,630 --> 00:01:07,214
so times 7 + g(1), which is -5 ...

20
00:01:07,214 --> 00:01:11,840
so + (-5) … which simplifies to – let's see ...

21
00:01:11,840 --> 00:01:20,298
-2 ×7 is -14 plus -5, which is -19.

22
00:01:20,298 --> 00:01:22,131
And we are done.