Answered

Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Given the function f(x) = 4(x+3) − 5, solve for the inverse function when x = 3

Sagot :

f(X)=4x+12-5=4x+7
so
{f(x)-7}/4=x
now in inverse func. f(x0 is converted into x and x is converted into
f(x)^-1
so
f(x)^-1=[x-7]/4
now if x=3
f(3)^-1=[3-7]/4=-4/4=-1

[tex]f(x)=4(x+3)-5\\ y=4(x+3)-5\\ y=4x+12-5\\ y=4x+7\\ 4x=y-7\\ x=\frac{1}{4}y-\frac{7}{4}\\ f^{-1}(x)=\frac{1}{4}x-\frac{7}{4}\\ f^{-1}(3)=\frac{1}{4}\cdot3-\frac{7}{4}\\ f^{-1}(3)=\frac{3}{4}-\frac{7}{4}\\ f^{-1}(3)=-\frac{4}{4}\\ f^{-1}(3)=-1[/tex]