The required function is [tex]y = -\frac{3}{2} x -36[/tex] having domain and range as R and y-intercept is -36.
Given function
y=f(x) = [tex]-\frac{2}{3} x -24[/tex]
An inverse function is a function that returns the original value for which a function has given the output. If f(x) is a function that gives output y, then the inverse function of y, i.e. f-1(y) will return the value x.
In order to get inverse function [tex]f^-1x[/tex] let us arrange the given function
[tex]y+24 = -\frac{2}{3} x[/tex]
[tex]x = -\frac{3}{2} y-36[/tex]
Now, replace x with y and vice versa.
[tex]y = -\frac{3}{2} x -36[/tex]........(1)
or, [tex]f^-1x = -\frac{3}{2} x -36[/tex]
(1) will be the inverse function of the given function.
For x-intercept put y = 0 and for y-intercept put x=0 in eq(1)
x-intercept = -24
y-intercept = -36
The domain and range of f⁻¹x = set of all real numbers since f⁻¹x is a straight line equation, domain, and range of which is set of all real numbers.
Therefore, the required function is [tex]y = -\frac{3}{2} x -36[/tex] having domain and range as R and y-intercept is -36.
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