Answer:
The inverse of the function is 
.
Step-by-step explanation:
The function provided is:
Let 
.
Then the value of <em>x</em> is:
For the inverse of the function, 
.
⇒
Compute the value of ![f[f^{-1}(x)]](https://tex.z-dn.net/?f=f%5Bf%5E%7B-1%7D%28x%29%5D)
as follows:
![f[f^{-1}(x)]=f[\frac{x-5}{3}]](https://tex.z-dn.net/?f=f%5Bf%5E%7B-1%7D%28x%29%5D%3Df%5B%5Cfrac%7Bx-5%7D%7B3%7D%5D)
![=3[\frac{x-5}{3}]+5\\\\=x-5+5\\\\=x](https://tex.z-dn.net/?f=%3D3%5B%5Cfrac%7Bx-5%7D%7B3%7D%5D%2B5%5C%5C%5C%5C%3Dx-5%2B5%5C%5C%5C%5C%3Dx)
Hence proved that ![f[f^{-1}(x)]=x](https://tex.z-dn.net/?f=f%5Bf%5E%7B-1%7D%28x%29%5D%3Dx)
.
Compute the value of ![f^{-1}[f(x)]](https://tex.z-dn.net/?f=f%5E%7B-1%7D%5Bf%28x%29%5D)
as follows:
![f^{-1}[f(x)]=f^{-1}[3x+5]](https://tex.z-dn.net/?f=f%5E%7B-1%7D%5Bf%28x%29%5D%3Df%5E%7B-1%7D%5B3x%2B5%5D)
Hence proved that ![f^{-1}[f(x)]=x](https://tex.z-dn.net/?f=f%5E%7B-1%7D%5Bf%28x%29%5D%3Dx)
.
Answer:
10 times as much
Step-by-step explanation:
the 2 in 82 is worth 2 ones while the 2 in 21 is worth 10 ones
r
sin
θ
=
−
3
Explanation:
Imagine we have a point
P
with Rectangular (also called Cartesian) coordinates
(
x
,
y
)
and Polar coordinates
(
r
,
θ
)
.
The following diagram will help us visualise the situation better:
https://keisan.casio.com/exec/system/1223526375
https://keisan.casio.com/exec/system/1223526375
We can see that a right triangle is formed with sides
x
,
y
and
r
, as well as an angle
θ
.
We have to find the relation between the Cartesian and Polar coordinates, respectively.
By Pythagora's theorem, we get the result
r
2
=
x
2
+
y
2
The only properties we can say about
θ
are its trigonometric functions:
sin
θ
=
y
/
r
⇒
y
=
r
sin
θ
cos
θ
=
x
/
r
⇒
x
=
r
cos
θ
So we have the following relations:
⎧
⎪
⎨
⎪
⎩
r
2
=
x
2
+
y
2
y
=
r
sin
θ
x
=
r
cos
θ
Now, we can see that saying
y
=
−
3
in the Rectangular system is equivalent to say
r
sin
θ
=
−
3
Answer link
Jim G.
May 19, 2018
r
=
−
3
sin
θ
Explanation:
to convert from
cartesian to polar
∙
x
x
=
r
cos
θ
and
y
=
r
sin
θ
⇒
r
sin
θ
=
−
3
⇒
r
=
−
3
sin
θ
Sorry for the delay but I answered your question and the answer is -6xsquare +11x-4
