Answer:
15
Step-by-step explanation:
Given the function
[tex]f(x)=5x+a[/tex]
and [tex]f^{-1} (10)=-1(f^{-1} \text{is the inverse function of f})[/tex]
let f(x)=y
Substitute in f(x)
[tex]y=5x+a\\y-a=5x\\x=\frac{y-a}{5}[/tex]
From the definition inverse function
if [tex]f(x)=y [/tex] ⇒ [tex]f^{-1} (y)=x[/tex]
Substitute this in the above expression
[tex]f^{-1} (y)=\frac{y-a}{5}[/tex]
Substitute y=10
⇒
[tex]f^{-1} (10)=\frac{10-a}{5}\\-1=\frac{10-a}{5}\\-5=10-a\\a=10+5\\a=15[/tex]
Therefore a=15
