Question

If F(x+1)= x2+1 then F(X) =

Answer 1

f

−

1

(

x

)

=

±

√

x

+

1

Explanation:

Let

y

=

f

(

x

)

.

Then,

y

=

x

2

−

1

To determine the inverse function, switch the places of

x

and

y

, and subsequently solve for

y

:

x

=

y

2

−

1

y

2

=

x

+

1

y

=

±

√

x

+

1

Since this is the inverse,

y

=

f

−

1

(

x

)

:

f

−

1

(

x

)

=

±

√

x

+

1