what is the inverse of f(x) = x^2 + 2 ?

Question

Hi, I just need to find the inverse of f(x) = x^2 + 2. So, can you help me ?

Answer 1

ƒ(x) = y = x² + 2
ƒ ^-1 (x) — ?

1. Let's solve given equation for x
y = x² + 2
x² = y - 2 Important condition: y - 2 ≥ 0 ---> y ≥ 2
x = √ (y - 2) 
2. Let's "switch" places for "x" and "y"
y =  √(x - 2)  with important condition: x ≥ 2 and y ≥ 0  —  the inverse function to the original one.

Answer 2

Hello Raheem,

The inverse of the f(x)=x²+2 is the square root of (f(x)-2), and we check it by plugging in a value for x for both the original and inverse function

F(4)=x²+2                   F ^-1(4)= (f(x)-2)^1/2

F(4)=4² +2                 F ^-1(4)= (f(x²+2)-2)^1/2

F(4)=16+2                 F  ^-1(4)= (f(4²+2-2) ^1/2

F(4)=18                    F ^-1(4)=(16)^1/2

                               F^-1(4)=4

The inverse formula is correct because it brought us back to the original value of x, which in this example was 4.

 

Answer 3

f(x) = x^2 + 2, so subtracting 2 from both sides

f(x) - 2 = x^2, and taking the square root of both sides

s = +- sqrt( f(x) - 2 )