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Svetradugi [14.3K]
2 years ago
6

Inverse of f(x) = x2 − 9

Mathematics
2 answers:
luda_lava [24]2 years ago
7 0
To find the inverse of a function, replace every x in the equation with a y, and replace every y in the equation with an x:

x = y^{2} - 9

Add 9 to both sides:

y^{2} = x + 9

Square root both sides to get y by itself:

y = \sqrt{x+9}

This equation can be simplified by taking the square root of 9 out of the root:

\sqrt{9} = 3
y = 3 + \sqrt{x}

The inverse of this function is y = 3 + √x.
Sophie [7]2 years ago
5 0
F(x) = x2 - 9
y = x2 - 9
y - 9 = x2
\sqrt{y - 9} = x

y = f(x)
f^(-1) (y) = x
f^(-1) (y) = \sqrt{y - 9}
f^(-1) (x) = \sqrt{x - 9}
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