SOLUTION: If f(x) = 1/4x+2 and g(x) = −3x^2+2, determine the value of -3 g(1) and f^-1 (1)

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Question 1182273: If f(x) = 1/4x+2 and g(x) = −3x^2+2, determine the value of -3 g(1) and f^-1 (1)
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
If f(x) = 1/4x+2 and g(x) = −3x^2+2, determine the value of -3 g(1) and f^-1 (1).
Let's separate the stating of the two problems:

If f(x) = (1/4)x+2, determine the value of f-1(1).
We find f-1(x)

a. Replace f(x) by y

y=expr%281%2F4%29%2Ax%2B2

b. Interchange x and y.

x=expr%281%2F4%29%2Ay%2B2

c. solve for y

Multiply through by 4 to clear the fraction:

4x+=+y%2B8

4x-8=y

y=4x-8

d. replace y by f-1(x)

f-1(x) = 4x-8

Therefore,

f-1(1) = 4(1)-8
f-1(1) = 4-8
f-1(1) = -4

--------------------------------
If g(x) = −3x2+2, determine the value of -3g(1).

   g(1) = −3(1)2+2
   g(1) = −3(1)+2
   g(1) = -3+2
   g(1) = -1

Therefore multiply both sides by -3:
 
 -3g(1) = -3(-1)
 -2g(1) = 3

Edwin