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photoshop1234 [79]
3 years ago
8

Suppose that the function g is defined, for all real numbers, as follows.

Mathematics
1 answer:
svetoff [14.1K]3 years ago
7 0

Answer:

<em>a) g(-2) = 0</em>

<em>b) g(-1) =1</em>

<em>c) g(4) = 2</em>

Step-by-step explanation:

Given data

g(x) = \frac{-1}{4x+1} if x < -2

g(x) = - (x+1)^{2} +1  if -2\leq x\leq 2

g(x) = 2 if x >2

<u><em>Step( i )</em></u>:-

g(x) = - (x+1)^{2} +1  if -2\leq x\leq 2

put x = -2

g(-2) = -(-2+1)^{2} +1 = -(-1)^{2}+1 = -1+1 =0

<em>g(-2) = 0</em>

<u><em>Step(ii)</em></u>:-

g(x) = - (x+1)^{2} +1  if -2\leq x\leq 2

Put x = -1

g(-1) = -(-1+1)^{2} +1 = -(0)^{2}+1 = -0+1 =1

<em>g(-1) =1</em>

<u><em>Step(iii)</em></u>:-

g(x) = 2 if x >2

<em>g(4) = 2</em>

<em></em>

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