Question

30 POINTS!!! i need help finding the inverse function in slope-intercept form ( mx+b )

Answer 1

`f^(-1)(x)=-(2)/(5)x+2}`

Explanation:

Find the inverse of the function.

`f(x)=(5)/(2)x+5`

(1) - Switch f(x) and x

`f(x)=-(5)/(2)x+5\\\\\Longrightarrow x=-(5)/(2)f(x)+5`

(2) - Solve for f(x)

`x=-(5)/(2)f(x)+5\\\\\Longrightarrow (5)/(2)f(x)=5-x\\\\\Longrightarrow f(x)=(2)/(5)(5-x)\\\\\Longrightarrow f(x)=(10)/(5)-(2)/(5)x \\\\\Longrightarrow f(x)=-(2)/(5)x+2`

(3) - Replace f(x) with f^-1(x)

`\therefore \boxed{f^(-1)(x)=-(2)/(5)x+2}`

Thus, the inverse is found.