Question
Asked Oct 11, 2019
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Use f(x) 2x - 4 and g(x) = 5 - x2 to evaluate the expression
(a)
(fo (x)
(b)
(g o g)(x)
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Use f(x) 2x - 4 and g(x) = 5 - x2 to evaluate the expression (a) (fo (x) (b) (g o g)(x)

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Expert Answer

Step 1

Given f(x) and g(x)

f(x) 2x-4
g(x) = 5-x
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f(x) 2x-4 g(x) = 5-x

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Step 2

(fof)(x)= f(f(x)). Substitute f(x) in f(x) itself

f(x)= 2x-4
(fof(x) f(f(x)) = f(2x-4)
2(2r-4)-4
(fof )(x)= 4x -8-4 4
-12
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f(x)= 2x-4 (fof(x) f(f(x)) = f(2x-4) 2(2r-4)-4 (fof )(x)= 4x -8-4 4 -12

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Step 3

(gog)(x)= g(g(x)). Substitut...

g(x) = 5-1
(gog)(x) = g(g(x)) = f(5-x)=5-(5-x2)
(gog)(x)=5-(5-x)=5-(5-x")(5-x)
(gog)(x)-5-(5-x(5-x')=5-(25-5x -5x +x*)
(gog)(x) 5-25+ 10x2 - x4 = -r4 +10x2 -20
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g(x) = 5-1 (gog)(x) = g(g(x)) = f(5-x)=5-(5-x2) (gog)(x)=5-(5-x)=5-(5-x")(5-x) (gog)(x)-5-(5-x(5-x')=5-(25-5x -5x +x*) (gog)(x) 5-25+ 10x2 - x4 = -r4 +10x2 -20

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Tagged in

Math

Calculus

Functions