Question

Explain what do you mean by a one to one funtion?

b) Explain briefly in steps how you would determine the inverse of a function f(x)

c) Find the inverse of the function
f(x)= x-1
the x-1 is in the square root formation

Answer 1

a) as i think , I'm not sure .. each value of x gives one value to y and each value of y gives one value of x .

b) solution is ...
Put x on one side and y on the other side of equation .. and to make the function details by y only

c)
f(x)=(x−1)2

y=(x−1)2

take root for both sides
√y=(x−1)

Put x on part and y on the other part .. and to make the function details by y only.
x=√y+1

Answer 2

I believe the originial function is
\[f(x)=\sqrt{x-1}\]
to find the inverse
rewrite as
\[y=\sqrt{x-1}\]
switch the x and y
\[x=\sqrt{y-1}\]
Solve for y
\[x=\sqrt{y-1}\]
\[\left( x \right)^2=\left( \sqrt{y-1} \right)^2\]
x=y-1
add 1 to both sides
x+1=y
your inverse is
\[ f \left( x \right)^{-1}=x+1\]

Answer 3

\[f^{-1}(x)=x^2+1\quad,\quad x\ge 0\]

Answer 4

NikVist ? how you Find that answer ?

Answer 5

yes I am sorry.
You are correct in correcting my last step
I dropped the 2nd power
all of my steps are correct.
\[x^2=y-1\]
add 1 to both sides
\[x^2+1=y\]
This is the inverse
\[f \left( x \right)^{-1}=x^2+1\]