1. Let f(x) = √ x + 1 − 1 4−x2 . Compute the following: (10 points)
i. f(0)
ii. f(-3)
iii. f(2)
iv. f(-1)
v. f(3)
vi. Domain(f(x))
2. (a) Let f( x x−2 ) = 3x + 4 find f(x).
(b) Compute difference quotient of the function g(x) = √ x2 − 9, and simplify your answer.
3. Let f(x) = 1 − x, g(x) = x2 + bx + c. find b and c such that fog(x) = −x2 + 5x + 4. + bx + c. find b and c such that fog(x) = −x2+ 5x + 4.
1
Expert's answer
2021-01-29T12:45:51-0500
1. f(x)=x+1−14−x2
i) -13
ii) not exist
iii) 3−18
iv) -15
v) -21
vi) [−1;+∞)
Explanation :
i) f(0)=0+1−14−02=1−14=−13 ii) f(−3)=−3−1−14−(−3)2=−4−14−9= - not defined) because −4 is not defined iii) f(2)=2+1−14−(2)2=3−14−4=3−18 iv) f(−1)=−1+1−14−(−1)2=0−14−1=−15 v) f(3)=3+1−19−32=2−14−9=−21 vi) x+1 needs x+1⩾0 , so domain is x∈[−1;+∞)
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