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Given f(x)=((1)/(2))^x. Determine the equation of the inverse function f⁻¹ in form x = .... Draw a neat graph of f for and f⁻¹ on the same system of axes in ADDENDUM 1.

October 1, 2026Mathematics

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Answer

x = \left(\frac{1}{2}\right)^y

Graph of f(x) = (1/2)^x

Key points of f(x) = (1/2)^x
Point	x	y
y-intercept	0	1

2 steps

To determine the equation of the inverse function $f^{-1}$ for $f(x) = \left(\frac{1}{2}\right)^x$ in the form $x = \dots$ :

Replace $f(x)$ with $y$ .
$y = \left(\frac{1}{2}\right)^x$
To find the inverse function, swap the variables $x$ and $y$ .
$x = \left(\frac{1}{2}\right)^y$
This equation represents the inverse function and is in the requested form $x = \dots$ .

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