Question

If f(x)=(1/2)x-3 and g(x)=2x+6 what is f(g(4))+g(f(4))

Answer 1

see explanation

Explanation:

To evaluate f(g(4)) substitute x = 4 into g(x) and then substitute the value obtained into f(x)

g(4) = (2 × 4) + 6 = 8 + 6 = 14, then

f(14) = (0.5 × 14) - 3 = 7 - 3 = 4

Hence f(g(4)) = 4

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To evaluate g(f(4)) substitute x = 4 into f(x) and then substitute the value obtained into g(x)

f(4) = (0.5 × 4) - 3 = 2 - 3 = - 1, then

g(- 1) = (2 × - 1) + 6 = - 2 + 6 = 4

Hence g(f(4)) = 4

Answer 2

given,

f(x)=(1/2)x-3

g(x)=2x+6

Now,

f(4)=(1/2)×4-3

=2-3=-1

g(4)=2×4+6=14

Then,

f(g(4))=f(14)=(1/2)×14-3=7-3=4

g(f(4))=g(-1)=2×(-1)+6=-2+6=4