Question

2) If f(x)=9-5x
then f-1(-1)​

Answer 1

Step-by-step explanation:

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hope it completely helps you....

Answer 2

The Value of $f^{-1}$(-1) = 2

As per the data given in the question.

We have to find the value of $f^{-1}$(-1), (Where  $f^{-1}$ is the invers function.)

As per the question,

It is given that in the question,

f(x) = 9-5x.

Here f(x) is a real valued function of x, where domain is x and range are f(x) and we can take y = f(x).

As, we know by the theorem of invers function we can conclude:

"If f(x) = y then $f^{-1}$(y) = x or If $f^{-1}$(y) = x then f(x) = y" that is "f(x) =y ⇔ $f^{-1}$(y) = x".

Using this concept, we can find $f^{-1}$(x), then $f^{-1}$(-1).

Then, f(x) = y = 9-5x

             ⇒ 5x = 9-y

            ⇒ x = $\frac{9-y}{5}$

           ⇒ $f^{-1}$(y) = $\frac{9-y}{5}$

If y = -1 then, $f^{-1}$(-1) = $\frac{9-(-1)}{5}$ = $\frac{10}{5}$ = 2

So, $f^{-1}$(-1) = 2

Ans = 2

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