F(x) = 4x+c and f^-1(x) = mx - 5/4. Find the values of m and c.?

f(x) = 4x+c


Let y = 4x+c


y-c = 4x


y-c/4 = x





Therefore, f^-1(x) = x-c/4





What do I do next?

F(x) = 4x+c and f^-1(x) = mx - 5/4. Find the values of m and c.?
You have done it wrong


f(x) = 4x+c


Let y = 4x+c


y-c = 4x


y-c/4 = x


--------------------------------------...


how is this possible


y-c = 4x


then


x = y/4 - c/4


so,


f^-1(x) = x/4 - c/4-------------%26gt;%26gt;(1)





given that





f(x) = 4x+c


and


f^-1(x) = mx - 5/4---------%26gt;%26gt;(2)





Comparing (1) and (2) we get





m = 1/4 and c = 5


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Hope this will help u...................
Reply:You know that both


:A: f^-1(x)=x-c/4 [what you derived from f(x)=4x+c]


and


:B: f^-1(x)=mx-5/4 [given]


are true. The only possible solution here is (m,c)=(1,5); substituting m=1 would give


:A: f^-1(x)=x-c/4


:B: f^-1(x)=x-5/4


and substituting c=5 would give


:A: f^-1(x)=x-5/4


:B: f^-1(x)=x-5/4