Given function is [tex] a(b)=10*\frac{b+7}{2} [/tex]
Or, [tex] a=10*\frac{b+7}{2} [/tex]
First step is to find the inverse is switch a and b. Therefore, the above equation will be:
[tex] b=10*\frac{a+7}{2} [/tex]
b = 5*(a + 7) By simplifying.
b = 5a + 35
Next step is to solve the equation for a to get the inverse of a (b). So, subtract 35 from each sides to isolate a. Hence,
b - 35 = 5a
[tex] \frac{b-35}{5} =\frac{5a}{5} [/tex]
[tex] \frac{b}{5} -\frac{35}{5}=a [/tex]
[tex] \frac{b}{5} - 7 = a [/tex]
Therefore , the inverse is [tex] b(a)=\frac{a}{5} - 7 [/tex].
So, c is the correct choice.
