Answer:
The slope of f(x) is inverse of the slope of f^-1(x)
Explanation:
The given function is:
[tex]f(x)=\frac{3}{4}x-5[/tex]
The function is of the form f(x) = mx + c
where m is the slope
Comparing f(x) =(3/4)x - 5 and f(x) = mx + c:
The slope, m = 3/4
The slope of f(x) = 3/4
The inverse of f(x) is calculated below
[tex]\begin{gathered} f(x)=\frac{3}{4}x-5 \\ \frac{3}{4}x=f(x)+5 \\ 3x=4(f(x))+20 \\ x=\frac{4}{3}f(x)+\frac{20}{3} \\ f^{-1}(x)=\frac{4}{3}x+\frac{20}{3} \end{gathered}[/tex]
The slope of f^-1(x) = 4/3
Note that 3/4 and 4/3 are inverse of each other
Therefore, the slope of f(x) is inverse of the slope of f^-1(x)
