SOLUTION: for the given funtions f and g, find (a) (f o g)(4) (b)(f o g)(2) (c)(f o f)(1) f(x)=2x; g(x)=3-1/2x^2

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Question 42289: for the given funtions f and g, find
(a) (f o g)(4) (b)(f o g)(2) (c)(f o f)(1)
f(x)=2x; g(x)=3-1/2x^2
Answer by nik_consult(24) About Me  (Show Source):
You can put this solution on YOUR website!
for the given funtions f and g, find
(a) (f o g)(4) (b)(f o g)(2) (c)(f o f)(1)
f(x)=2x; g(x)=3-1/2x^2
solution:
(a) g(4)= 3-1/2(4)^2
= 3- 1 / 32
= 2%2831%29%2F%2832%29
so, (f o g)(4)= f[g(4)]
= f[2%2831%29%2F%2832%29]
= 2 x [2%2831%29%2F%2832%29]
= 5%2815%29%2F%2816%29
(b)g(2)= 3-1/2(2)^2
= 3-1/8
= 2%287%29%2F%288%29
so,(f o g)(2)= f[g(2)]
= f[2%287%29%2F%288%29]
= 2 x 2%287%29%2F%288%29
= 5%283%29%2F%284%29
(c)f(1)= 2(1)=2
so, (f o f)(1)= f[f(1)]
= f[2]
= 2(2)
= 4