# PLEASE HELP ME OUT !!!!!!!! 20 POINTSSSSSS

Question

Answer:

Step OneFor convenience f(x) = y

y = -(1/2) sqrt(x + 3) Interchange x and y

x = -(1/2) sqrt(y + 3) Multiply both sides by -2

(-2x) = sqrt(y + 3) Square both sides

4x^2 = y + 3 Subtract 3 from both sides

4x^2 -3 = y

f-1(x) = 4x^2 - 3

Graphs

The original graph is in blue

The inverse is red.

Green Line y = x : explained below.

Comment

Inverses have a very strange property. It acts as a check.

If you perform the following operation

f-1(f(x)) you are left with x

In this case f-1[-1/2 sqrt(x + 3)]= 4(-1/2 * sqrt(x + 3))^2 - 3

f-1 (-1/2sqrt(x+3)) = 4 (1/4 (x+3) - 3

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

I've included this because I think you have to put the same restriction on f-1(x) as you do on f(x) which is that for f(x) x ≥ -3

This last assertion could be incorrect, but I don't think so.

The answer is f-1(x) = 4x^2 - 3 <<<<< answer first box and

x≥-3 for the second box. <<<<<< answer for the second box.

Let me know if these are correct. I'm not sure about the restrictions.

solved

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2 months ago
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