Given:
The function is
[tex]F(x)=\dfrac{2}{7}x+4[/tex]
To find:
The inverse function of the given function.
Solution:
We have,
[tex]F(x)=\dfrac{2}{7}x+4[/tex]
Putting F(x)=y, we get
[tex]y=\dfrac{2}{7}x+4[/tex]
Interchange x and y.
[tex]x=\dfrac{2}{7}y+4[/tex]
Subtract 4 from both sides.
[tex]x-4=\dfrac{2}{7}y[/tex]
Multiply both sides by 7.
[tex]7(x-4)=2y[/tex]
[tex]7x-28=2y[/tex]
Divide both sides by 2.
[tex]\dfrac{7x-28}{2}=y[/tex]
[tex]\dfrac{7}{2}x-14=y[/tex]
[tex]y=\dfrac{7}{2}x-14[/tex]
Putting [tex]y=F^{-1}(x)[/tex], we get
[tex]F^{-1}(x)=\dfrac{7}{2}x-14[/tex]
Therefore, the required inverse function is [tex]F^{-1}(x)=\dfrac{7}{2}x-14[/tex].
