Question

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

Answer 1

Answer:

15

Step-by-step 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)

$y=5x+a\\y-a=5x\\x=\frac{y-a}{5}$

From the definition inverse function

if $f(x)=y$    ⇒   $f^{-1} (y)=x$

Substitute this in the above expression

$f^{-1} (y)=\frac{y-a}{5}$

Substitute y=10

⇒

$f^{-1} (10)=\frac{10-a}{5}\\-1=\frac{10-a}{5}\\-5=10-a\\a=10+5\\a=15$

Therefore a=15