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Alex777 [14]
3 years ago
14

Find the inverse of the given function. f(x) = -1/2√x + 3, x ≥ -3

Mathematics
2 answers:
shepuryov [24]3 years ago
5 0

Answer:

The inverse of the function is f^{-1}(x)=4x^2-3, for x\leq 0

Step-by-step explanation:

Given : Function f(x)=-\frac{1}{2}\sqrt{x+3}

To find : The inverse of the given function?

Solution :  

To find the inverse of the function we replace the value of x and y and then find y in terms of x which is the inverse of the function.

Let f(x)=y

y=-\frac{1}{2}\sqrt{x+3}                

Replace the value of x and y.

x=-\frac{1}{2}\sqrt{y+3}                  

Now, we solve in terms of x the value of y

-2x=\sqrt{y+3}  

(x must be negative)

Squaring both side,

(-2x)^2=(\sqrt{y+3})^2  

4x^2=y+3  

4x^2-3=y  

So, The inverse of the function is f^{-1}(x)=4x^2-3, for x\leq 0

inna [77]3 years ago
4 0
<span>Find the inverse of the given function.

f(x) = -1/2√x + 3, x ≥ -3

I will have to assume that you meant f(x) = -(1/2)sqrt(x) + 3.  If you actually meant f(x) = -(1/2)sqrt(x+3), then obviously the correct result would be different.

1.  Replace "f(x)" by "y:"  y </span>= -(1/2)sqrt(x) + 3
 2.  Interchange x and y:  x = -(1/2)sqrt(y) + 3
3.  Solve for y:  x-3=-(1/2)sqrt(y), so that 2(3-x)= sqrt(y) and y=+sqrt(2[3-x])
4.  Replace "y" with 

           -1
        f      (x) = sqrt(2[3-x])

Here, there are restrictions on x, since the domain of the sqrt function does not include - numbers.  The domain here is (-infinity,3]
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