Question

If f(x)=5x+a and f-1(10)=-1, find a

Answer 1

15

Explanation:

Given the function

`f(x)=5x+a`

and
`f^(-1) (10)=-1(f^(-1) \text{is the inverse function of f})`

let f(x)=y

Substitute in f(x)

`y=5x+a\\y-a=5x\\x=(y-a)/(5)`

From the definition inverse function

if
`f(x)=y` ⇒
`f^(-1) (y)=x`

Substitute this in the above expression

`f^(-1) (y)=(y-a)/(5)`

Substitute y=10

⇒

`f^(-1) (10)=(10-a)/(5)\\-1=(10-a)/(5)\\-5=10-a\\a=10+5\\a=15`

Therefore a=15